In the figure R1 = 10.4 kΩ, R2 = 14.1 kΩ, C = 0.402 μF, and the ideal battery has emf E = 22.0 V. First, the switch is closed a long time so that the steady state is reached. Then the switch is opened at time t = 0. What is the current in resistor 2 at t = 4.50 ms?
Below is a depiction of a mass-spectrometer, the charged particle enters the velocity selector, which as an Electric field (E) and Magnetic Field (B), and then once in the Detector array (with Magnetic Field B0) the charge follows a circular path until it hits the detector array. If an electron is sent thru the selector and hits the array at a radius (r), calculate the Ratio E/B.
Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.175 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 0.970 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object, the answer to part (a) being the one with the greater (and positive) value? (a) Number Units (b) Number Units
In the figure, block 2 of mass 2.30 kg oscillates on the end of a spring in SHM with a period of 30.00 ms. The position of the block is given by x = (0.500 cm)cos(ωt + π/2). Block 1 of mass 4.60 kg slides toward block 2 with a velocity of magnitude 8.70 m/s, directed along the spring's length. The two blocks undergo a completely inelastic collision at time t = 7.50 ms. (The duration of the collision is much less than the period of motion. ) What is the amplitude of the SHM after the collision? Number Units
A system gains 3400 J of heat at a constant pressure of 1.33×105 Pa, and its internal energy increases by 4000 J. What is the change in the volume of the system, and is it an increase or a decrease? ΔV =
A 354-g object is attached to a spring and executes simple harmonic motion with a period of 0.240 s. If the total energy of the system is 5.76 J, find the following. (a) the maximum speed of the object m/s (b) the force constant of the spring N/m (c) the amplitude of the motion m
A 2.600-kg model rocket is launched vertically and reaches an altitude of 70 m with a speed of 30 m/s at the end of powered flight, time t = 0. As the rocket approaches its maximum altitude it explodes into two parts of masses mA = 0.910 kg and mB = 1.690 kg. Part A is observed to strike the ground 80 m west of the launch point at t = 6 s. Determine the position of part B at that time. The position of part B is m (east) and m (up).
In the figure, block 2 of mass 2.20 kg oscillates on the end of a spring in SHM with a period of 18.00 ms. The position of the block is given by x = (1.10 cm)cos(ωt + π/2). Block 1 of mass 4.40 kg slides toward block 2 with a velocity of magnitude 6.30 m/s, directed along the spring's length. The two blocks undergo a completely inelastic collision at time t = 4.50 ms. (The duration of the collision is much less than the period of motion. ) What is the amplitude of the SHM after the collision? Number Units
A 50 lb child is sitting on one end of a seesaw, 3 ft from the center fulcrum. (See Figure 1.69.) When she is 1.5 ft above the horizontal position, what is the amount of torque she exerts on the seesaw?
An 8 kg object experiences a varying force according to the function shown in the Force vs time graph below. What is the total change in momentum of the object during the first 5 seconds? 280 kg⋅m/s 200 kg⋅m/s 150 kg⋅m/s 240 kg⋅m/s 35 kg⋅m/s
In the first figure, a block of mass m lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant k) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x = 0) when a constant horizontal force in the positive direction of the x axis is applied to it. A plot of the resulting kinetic energy of the block versus its position x is shown in the second figure. The scale of the figure's vertical axis is set by Ks = 8.0 J. (a) What is the magnitude of F→? (b) What is the value of k? (a)
A 12.4 kg block is pulled by a force of 26.8 N across a horizontal table. The coefficient of static friction is 0.4. The coefficient of kinetic friction is 0.2. What is the static friction force experienced by the block? Do not include units in your answer (enter a numerical result only).
A block of mass m is placed on a horizontal track of negligible friction. The mass is pushed against a spring and released (the mass is not attached to the spring). The block then slides up a rough incline plane of coefficient of kinetic friction μ and angle θ = arctan(3/4). Assuming the spring constant is k = 18 mg/h, what distance must the spring be compressed so that the block's maximum height is h? Express your result in terms of the given quantities and any numerical and physical constants.
The only force acting on a 1.5 kg body as it moves along the positive x axis has an x component Fx = −6x N, where x is in meters. The velocity of the body at x = 2.5 m is 8.4 m/s. (a) What is the velocity of the body at x = 4.4 m? (b) At what positive value of x will the body have a velocity of 5.0 m/s? (a) Number Units (b) Number Units
A conservative force F(x) acts on a 1.5 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is graphed in the figure. When the particle is at x = 2.0 m, its velocity is −1.4 m/s. (a) What is F(x) at this position, including sign? Between what positions on the (b) left and (c) right does the particle move? (d) What is its particle's speed at x = 7.0 m? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A 5.0 kg toy car can move along an x axis. The figure gives Fx of the force acting on the car, which begins at rest at time t = 0. The scale on the Fx axis is set by FXS = 4.0 N. In unit-vector notation, what is P→ at (a)t = 1.0 s and (b) t = 7.0 s, (c) what is v→ at t = 4.0 s? (a) Number i^ + j^ + k^ Units (b) Number i^ + j^ + k^ Units (c) Number i^ + j^ + k^ Units
A woman is 1.7 m tall and has a mass of 51 kg. She moves past an observer with the direction of the motion parallel to her height. The observer measures her relativistic momentum to have a magnitude of 2.3×1010 kg⋅m/s. What does the observer measure for her height? Number Units
Tarzan, who weighs 647 N, swings from a cliff at the end of a convenient vine that is 13.7 m long (see the figure). From the top of the cliff to the bottom of the swing, he descends by 1.66 m. The vine will break if the force on it exceeds 1030 N. What would the greatest force on the vine be during the swing? Number Units
The figure shows a rigid assembly of a thin hoop (of mass m = 0.29 kg and radius R = 0.15 m) and a thin radial rod (of length L = 2R and also of mass m = 0.29 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?
A 65.0 kg person running at an initial speed of v1 = 4.10 m/s jumps onto a m = 130 kg cart initially at rest. (Figure P9.55) The person slides on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.410 . Friction between the cart and ground can be neglected. Figure P9.55 (a) Find the final velocity of the person and cart relative to the ground. m/s (b) Find the frictional force acting on the person while he is sliding across the top surface of the cart. N (c) How long does the frictional force act on the person? s (d) Find the change in momentum of the person and the change in momentum of the cart. N⋅s (person) N. s (cart) (e) Determine the displacement of the person relative to the ground while he is sliding on the cart. m (f) Determine the displacement of the cart relative to the ground while the person is sliding. m (g) Find the change in kinetic energy of the person. (h) Find the change in kinetic energy of the cart. J (i) Explain why the answers to (g) and (h) differ. (What kind of collision is this, and what accounts for the loss of mechanical energy?)
A 0.64 kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing. Determine the following. (a) amplitude A of the motion m (b) angular frequency ω rad/s (c) spring constant k N/m (d) speed of the object at t = 0.500 s m/s (e) magnitude of the object's acceleration at t = 0.500 s m/s2
2 . A 1.25 kg ball is attached to a spring and describes a horizontal circle, as illustrated. At the moment shown, the length of the spring is 0.83m and θ = 35∘ /2 a. Draw a free-body diagram of the ball. /3 b. Find the magnitude of the force that the spring exerts on the ball. /3 c. Find the angular speed of the system. /2 d. Find the natural length of the spring if k = 150 N/m. (2 pts)
Consider the circuit shown in the figure. A short time after closing the switch, the charge on the capacitor is 55.0% of its initial charge. Assume the circuit has a time constant of 19.7 s. (a) Calculate the time interval required (in s) for the capacitor to reach this charge. s (b) If R = 240 kΩ, what is the value of C (in μF)? μF
A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 51.6 m. At the instant it makes an angle of 30.0∘ with the vertical as it falls, what are (a) the radial acceleration of the top, and (b) the tangential acceleration of the top. (Hint: Use energy considerations, not a torque.) (c) At what angle θ is the tangential acceleration equal to g? Assume free-fall acceleration to be equal to 9.81 m/s2.
A car travels at a constant speed of 30.0 mi/h (13.4 m/s) on a level circular turn of radius 50.0 m. What minimum coefficient of static friction, μs, between the tires and roadway will allow the car to make the circular turn without sliding?
In the figure battery 1 has emf E1 = 25.0 V and internal resistance r1 = 0.023 Ω and battery 2 has emf E2 = 25.0 V and internal resistance r2 = 0.019 Ω. The batteries are connected in series with an external resistance R. (a) What R value makes the terminal-to-terminal potential difference of one of the batteries zero? (b) Which battery is that? (a) Number Units (b)
The masses and coordinates of four particles are as follows: 52 g, x = 1.0 cm, y = 1.0 cm;18 g, x = 0, y = 2.0 cm;43 g, x = −1.5 cm, y = −1.5 cm;52 g, x = −1.0 cm, y = 2.0 cm. What are the rotational inertias of this collection about the (a) x, (b) y, and (c) z axes? (a) Number Units (b) Number Units (c) Number Units
In the figure the current in resistance 6 is i6 = 1.35 A and the resistances are R1 = R2 = R3 = 2.13 Ω, R4 = 18.0 Ω, R5 = 7.93 Ω, and R6 = 4.38 Ω. What is the emf of the ideal battery? Number Units
A 75.0-Ω and a 60.0-Ω resistor are connected in parallel. When this combination is connected across a battery, the current delivered by the battery is 0.166 A. When the 60.0-Ω resistor is disconnected, the current from the battery drops to 0.0770 A. Determine (a) the emf and (b) the internal resistance of the battery. (a) Number Units (b) Number Units
The drawings show three charges that have the same magnitude but may have different signs. In all cases the distance d between the charges is the same. The magnitude of the charges is |q| = 8.6 μC, and the distance between them is d = 6.6 mm. Determine the magnitude of the net force on charge 2 for each of the three drawings.
The circuit as shown in the Figure above shows a capacitor C, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, by how much does the charge on the capacitor change? Assume C = 54 μF, ε1 = 2.7 V, ε2 = 0.92 V, R1 = 0.16 Ω, and R2 = 0.78 Ω. a. 320.93 μC b. 162.21 μC c. 79.76 μC d. 760.46 μC e. 245.93 μC
The drawing shows a frictionless incline and pulley. The two blocks are connected by a wire (mass per unit length = 0.0214 kg/m) and remain stationary. A transverse wave on the wire has a speed of 65.5 m/s. Neglecting the weight of the wire relative to the tension in the wire, find the masses (a) m1 and (b) m2 of the blocks. (a) Number Units (b) Number Units
The figure gives the electric potential V(x) along a copper wire carrying uniform current, from a point of higher potential VS = 8.00 μV at x = 0 to a point of zero potential at xs = 2.40 m. The wire has a radius of 2.10 mm, and copper has a resistivity of 1.69×10−8 Ω⋅m. What is the current in the wire?
The electronic flash attachment for a camera contains a capacitor for storing the energy used to produce the flash. In one such unit, the potential difference between the plates of an 1100−μF capacitor is 430 V. (a) Determine the energy that is used to produce the flash in this unit. (b) Assuming that the flash lasts for 5.6 ms, find the effective power or "wattage" of the flash. (a) Number Units (b) Number Units
You attach one end of a spring with a force constant k = 753 N/m to a wall and the other end to a mass m = 1.92 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position xi = 6.56 cm from equilibrium and release it. (a) Determine the potential energy stored in the spring before the block is released. J (b) Determine the speed of the block as it passes through the equilibrium position. m/s (c) Determine the speed of the block when it is at a position xi/4. m/s
A positive point charge ( q = +5.62×10−8 C ) is surrounded by an equipotential surface A, which has a radius of rA = 1.66 m. A positive test charge (q0 = +3.12×10−11 C) moves from surface A to another equipotential surface B, which has a radius rB. The work done by the electric force as the test charge moves from surface A to surface B is WAB = −9.39×10−9 J. Find rB. rB =
Four long, parallel conductors carry equal currents of I = 8.00 A. The figure below is an end view of the conductors. The current direction is into the page at points A and B and out of the page at C and D. (i) (a) Calculate the magnitude of the magnetic field at point P, located at the center of the square of edge length ℓ = 0.200 m. μT (b) Determine the direction of the magnetic field at point P, located at the center of the square of edge length ℓ = 0.200 m. to the left to the right upward downward into the page out of the page (c) What If? What would be the magnitude and direction of the initial acceleration of an electron moving with velocity 2.93×105 m/s into the page at point P ? magnitude m/s2 direction
In the figure, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.0221 T. The loop consists of a single turn of flexible conducting wire that is wrapped around a flexible mount such that the dimensions of the rectangle can be changed. (The total length of the wire is not changed.) As edge length x is varied from approximately zero to its maximum value of approximately 2.84 cm , the magnitude T of the torque on the loop changes. The maximum value of T is 5.43×10−8 N∗m. What is the current in the loop? Number Units
In the figure the ideal batteries have emfs E1 = 24 V and E2 = 6.0 V and the resistors have resistances R1 = 4.1 Ω and R2 = 8.4 Ω. What are (a) the current, the energy dissipation rate in (b) resistor 1 and (c) resistor 2, and the energy transfer rate in (d) battery 1 and (e) battery 2? Is energy being supplied or absorbed by (f) battery 1 and (g) battery 2? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) g)
The figure shows a 11.1 V battery and four uncharged capacitors of capacitances C1 = 1.29 μF, C2 = 2.25 μF, C3 = 3.38 μF, and C4 = 4.23 μF. If only switch S1 is closed, what is the charge on (a) capacitor 1, (b) capacitor 2, (c) capacitor 3, and (d) capacitor 4? If both switches are closed, what is the charge on (e) capacitor 1, (f) capacitor 2, (g) capacitor 3, and (h) capacitor 4?
One heater uses 420 W of power when connected by itself to a battery. Another heater uses 310 W of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery? Number Units
The current through the battery and resistors 1 and 2 in Figure (a) is 1.90 A. Energy is transferred from the current to thermal energy Eth in both resistors. Curves 1 and 2 in Figure (b) give the thermal energy Eth dissipated by resistors 1 and 2, respectively, as a function of time t. The vertical scale is set by Eth,s = 66.0 mJ, and the horizontal scale is set by ts = 3.80 s. What is the power supplied by the battery? (a) (b) t(s) Number Unit
In the figure the current in resistance 6 is i6 = 1.45 A and the resistances are R1 = R2 = R3 = 2.22 Ω, R4 = 17.5 Ω, R5 = 7.71 Ω, and R6 = 3.90 Ω What is the emf of the ideal battery? Number Units
Two charges are located on the x axis: q1 = +5.5 μC at x1 = +5.0 cm, and q2 = +5.5 μC at x2 = −5.0 cm. Two other charges are located on the y axis: q3 = +3.8 μC at y3 = +4.8 cm, and q4 = −9.9 μC at y4 = +6.2 cm. Find (a) the magnitude and (b) the direction of the net electric field at the origin.
A wire of resistance 5.2 Ω is connected to a battery whose emf ε is 6.0 V and whose internal resistance is 0.60 Ω. In 2.6 min, how much energy is (a) transferred from chemical to electrical form in the battery, (b) dissipated as thermal energy in the wire, and (c) dissipated as thermal energy in the battery? (a) Number Units (b) Number Units (c) Number Units
A 12.0−V battery is connected to a pair of capacitors in parallel with capacitances CA = 9.40 μF and CB = 21.0 μF. (a) What is the equivalent capacitance of the pair of capacitors? μF (b) What charge is stored by each of the capacitors? QA = μC QB = μC (c) What is the potential difference across each of the capacitors? VA = V VB = V
In Figure (a), both batteries have emf E = 1.00 V and the external resistance R is a variable resistor. Figure (b) gives the electric potentials V between the terminals of each battery as functions of R: Curve 1 corresponds to battery 1 , and curve 2 corresponds to battery 2. The horizontal scale is set by Rs = 0.400 Ω. What is the internal resistance of (a) battery 1 and (b) battery 2? (a) (b) (a) Number Unit (b) Number Unit
In the figure the ideal batteries have emfs E1 = 9.0 V and E2 = 0.500E1, and the resistances are each 3.38 Ω. What is the value of current in (a) resistor 2 and (b) resistor 3? (a) Number Units (b) Number Units
The masses and coordinates of four particles are as follows: 35 g, x = 3.0 cm, y = 3.0 cm;29 g, x = 0, y = 6.0 cm;11 g, x = −4.5 cm, y = −4.5 cm;28 g, x = −3.0 cm, y = 6.0 cm. What are the rotational inertias of this collection about the (a) x, (b) y, and (c) z axes? (a) Number Units (b) Number Units (c) Number Units
The current through the battery and resistors 1 and 2 in Figure (a) is 3.00 A. Energy is transferred from the current to thermal energy Eth in both resistors. Curves 1 and 2 in Figure (b) give the thermal energy Eth dissipated by resistors 1 and 2, respectively, as a function of time t. The vertical scale is set by Eths, = 64.0 mJ, and the horizontal scale is set by ts = 4.70 s. What is the power supplied by the battery? (a) Number Number Unit
If the rigid body shown is subjected to a general plane motion with respect to the fixed coordinate system x−y, the velocity VA relative to VB (or VA/B) is zero ω×rB/A d(rA/B)/dt always ≠ 0 as long as rA/B ≠ 0.
In Figure (a) below, a 10.71 V battery is connected to a resistive strip that consists of three sections with the same cross-sectional areas but different conductivities. Figure (b) gives the electric potential V(x) versus position x along the strip. The horizontal scale is set by xs = 10.72 mm. Section 3 has conductivity 3.008×107(Ω⋅m)−1. What is the conductivity of section (a) 1 and (b) 2? (a) (a) Number Units (b) Number Units
In the figure R1 = 89 Ω, R2 = 59 Ω, and the ideal batteries have emfs ε1 = 7.0 V, ε2 = 6.0 V, and ε3 = 5.0 V. Find (a) the current in R1, (b) the current in R2, and (c) the potential difference between points a and b. (a) Number Units (b) Number Units (c) Number Units
Suppose the emf of the battery in the circuit shown in the figure varies with time t so that the current is given by i(t) = 3.00 + 4.00t, where i is in amperes and t is in seconds. Take R = 3.00 Ω and L = 4.00 H, and find the emf required of the battery at t = 4.00 s. Number Units
In the figure how much charge is stored on the parallel-plate capacitors by the 11.0 V battery? One is filled with air, and the other is filled with a dielectric for which k = 3.30; both capacitors have a plate area of 8.10×10−3 m2 and a plate separation of 8.60 mm. Number Units
In the figure particle 1 of charge +6e is above a floor by distance d1 = 4.80 mm and particle 2 of charge +7e is on the floor, at distance d2 = 7.00 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1? Number Units
The capacitors in the figure are initially uncharged. The capacitances are C1 = 4.2 μF, C2 = 6.5 μF, and C3 = 14 μF, and the battery's potential difference is V = 13 V. When switch S is closed, how many electrons travel through (a) point a, (b) point b, (c) point c, and (d) point d ? (e) In the figure, do the electrons travel up or down through point b? (f) In the figure, do the electrons travel up or down through point c? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) (f)
Three point charges are arranged as shown in the drawing. The value of q is 4.0 μC and the distance a is 20.0 cm. The point P is located a distance y = 35.0 cm along the y-axis. a. Determine the magnitude and direction of the electric field produced by the three charges at point P. (12) b. If an electron were placed at point P, what total electrostatic force would be exerted on the electron? (4)
In the figure the battery has potential difference V = 14.0 V, C2 = 3.50 μF, C4 = 4.30 μF, and all the capacitors are initially uncharged. When switch S is closed, a total charge of 10.0 μC passes through point a and a total charge of 9.00 μC passes through point b. What are (a) C1 and (b) C3?
The circuit shown below includes a battery of EMF = 9.419 V, resistors with R1 = 0.403 Ω and R2 = 0.583 Ω, and an inductor with L = 3.137 H. What is the inductive time constant for the growth of the current through the inductor when the switch in the figure is closed? s
The current through the battery and resistors 1 and 2 in Figure (a) is 2.90 A. Energy is transferred from the current to thermal energy Eth in both resistors. Curves 1 and 2 in Figure (b) give the thermal energy Eth dissipated by resistors 1 and 2 , respectively, as a function of time t. The vertical scale is set by Eth,s = 74.0 mJ, and the horizontal scale is set by ts = 5.80 s. What is the power supplied by the battery? (a) (b) t(s) Number Unit
A battery with E = 7.00 V and no internal resistance supplies current to the circuit shown in the figure below. When the double-throw switch S is open as shown in the figure, the current in the battery is 1.07 mA . When the switch is closed in position a, the current in the battery is 1.27 mA. When the switch is closed in position b, the current in the battery is 2.10 mA. Find the following resistances. (a) R1 kΩ (b) R2 kΩ (c) R3 kΩ
In the figure R1 = 140 Ω, R2 = R3 = 56.0 Ω, R4 = 69.9 Ω, and the ideal battery has emf ε = 6.00 V. (a) What is the equivalent resistance? What is in (b) resistance 1, (c) resistance 2, (d) resistance 3, and (e) resistance 4? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
In the figure the resistances are R1 = 1.4 Ω and R2 = 2.8 Ω, and the ideal batteries have emfs E1 = 1.7 V, and E2 = E3 = 4.5 V. What are the (a) size and (b) direction (up or down) of the current in battery 1, the (c) size and (d) direction of the current in battery 2, and the (e) size and (f) direction of the current in battery 3? (g) What is the potential difference Va−Vb? (a) Number Units (b) (c) Number Units (d) (e) Number Units (f) (g) Number Units
Consider the non-uniform charge distribution ρ(r) = ρ0r/R of an infinitely long cylinder of radius R . What is the electric force on a point charge q located at r where r < R? (Attention: Be sure to mark the correct answer. If you mark a wrong answer you will lose 20% of the pt.) a) qρ0ϵ0 r b) qρ02ϵ0 r c) qρ03ϵ0 Rr2 d) qρ02ϵ0 Rr2 e) qρ03ϵ0 Rr3
A straight current (i) carrying conductor (remaining circuit is not shown) and having a mass m is hinged at point on the boundary of magnetic field of intensity B as shown. The system lies in the x−y smooth horizontal plane. If the conductor is released, the angular acceleration of the conductor will be Only one correct answer A. 3iB 2m B. 3iB m C. 3iB 4m D. 3iB 2m
Calculate the magnitude of the magnetic field at point a in the figure. The current in the wires at y = 1.00 cm and y = −1.00 cm is 11.0 A. Magnitude:
At time t1, an electron is sent along the positive direction of an v axis, through both an electric field E and a magnetic field B with E directed parallel to the y axis. The figure gives the y component Fnet, y of the net force on the electron due to the two fields, as a function of the electron's speed v at time t1. The scale of the velocity axis is set by vs = 6.4 m/s. The x and z components of the net force are zero at t1. Assuming Bx = 0 find the magnitude of B in units of Tesla.
With the aid of a string, a gyroscope is accelerated from rest to 31 rad/s in 0.36 s. (a) What is its angular acceleration in rad/s2? rad/s2 (b) How many revolutions does it go through in the process? rev
In the figure, a climber with a weight of 390 N is held by a belay rope connected to her climbing harness and belay device; the force of the rope on her has a line of action through her center of mass. The indicated angles are θ = 35∘ and φ = 35∘. If her feet are on the verge of sliding on the vertical wall, what is the coefficient of static friction between her climbing shoes and the wall? μS = Number Units
A uniform spherical shell of mass M = 18.0 kg and radius R = 0.990 m can rotate about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.100 kg⋅m2 and radius r = 0.120 m, and is attached to a small object of mass m = 3.30 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen a distance 0.820 m after being released from rest? Use energy considerations.
A point magnetic dipole m in vacuum (medium 1) is pointing toward the plane surface of a medium with permeability μ (medium 2). The distance between the dipole and surface is d. (a) Solve for the magnetic field B within the medium. (b) What is the force acting on the dipole?
A beam of electrons is created by an electron gun and they move horizontally with a speed of 3.3×107 m/s. The electrons enter a 2.0 cm long gap between the two parallel plates where the electric field intensity is 5.0×104 N/C down. See the diagram below. a) Determine the time to cross the plates. b) Determine the magnitude and direction of the acceleration in the region between the plates. c) Determine the final velocity of the electron as it leaves the plates (both magnitude and direction).
A copper rod of mass m = 0.963 kg rests on two horizontal rails a distance L = 1.07 m apart and carries a current of i = 53.0 A from one rail to the other. A top view and a side view are shown in the figure. The coefficient of static friction between rod and rails is μ = 0.680. What are the (a) magnitude and (b) angle (relative to the vertical) of the smallest magnetic field that puts the rod on the verge of sliding? (a) Number Units (b) Number Units
An ice chest at a beach party contains 12 cans of soda at 3.43∘C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kgC∘). Someone adds a 6.82 - kg watermelon at 27.9∘C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon in degrees Celsius. Initial Final Number Units
An ice chest at a beach party contains 12 cans of soda at 2.47∘C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kgC∘). Someone adds a 8.53−kg watermelon at 27.7∘C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon in degrees Celsius. Initial Final Number Units
Review Conceptual Example 3 and the drawing as an aid in solving this problem. A conducting rod slides down between two frictionless vertical copper tracks at a constant speed of 5.6 m/s perpendicular to a 0.58−T magnetic field. The resistance of the rod and tracks is negligible. The rod maintains electrical contact with the tracks at all times and has a length of 1.1 m. A 1.1−Ω resistor is attached between the tops of the tracks. (a) What is the mass of the rod? (b) Find the change in the gravitational potential energy that occurs in a time of 0.28 s. (c) Find the electrical energy dissipated in the resistor in 0.28 s. (a) Number Units (b) Number Units (c) Number Units
A patient weighs 187 pounds and needs medication with dosage instructions of 15 mg/kg/day. It is to be given in 3 doses each day. How much medication should they receive per dose? Remember, 2.2 pounds is equal to 1 kilogram. Round to the nearest whole number. Provide your answer below: mg
A 10−mm diameter marble rolls off a horizontal step h = 4 m. Determine the minimum and maximum speed Vo the marble can have if it is to pass through a D = 200−mm wide hole and d = 2 m away from the bottom of the step.
In the figure below, a long circular pipe with outside radius R = 2.64 cm carries a (uniformly distributed) current i = 13.0 mA into the page. A wire runs parallel to the pipe at a distance of 3.00R from center to center. Find the (a) magnitude and (b) direction (into or out of the page) of the current in the wire such that the ratio of the magnitude of the net magnetic field at point P to the magnitude of the net magnetic field at the center of the pipe is 4.29, but it has the opposite direction. (a) Number Units (b)
In the figure below, a long circular pipe with outside radius R = 2.38 cm carries a (uniformly distributed) current i = 9.86 mA into the page. A wire runs parallel to the pipe at a distance of 3.00 R from center to center. Find the (a) magnitude and (b) direction (into or out of the page) of the current in the wire such that the ratio of the magnitude of the net magnetic field at point P to the magnitude of the net magnetic field at the center of the pipe is 2.48, but it has the opposite direction. (a) Number Units (b)
Light waves with two different wavelengths, 632 nm and 474 nm, pass simultaneously through a single slit whose width is 7.06×10−5 m and strike a screen 1.50 m from the slit. Two diffraction patterns are formed on the screen. What is the distance (in cm) between the common center of the diffraction patterns and the first occurrence of the spot where a dark fringe from one pattern falls on top of a dark fringe from the other pattern? Number Units
Light waves with two different wavelengths, 632 nm and 474 nm, pass simultaneously through a single slit whose width is 6.54×105 m and strike a screen 1.30 m from the slit. Two diffraction patterns are formed on the screen. What is the distance (in cm) between the common center of the diffraction patterns and the first occurrence of the spot where a dark fringe from one pattern falls on top of a dark fringe from the other pattern? Number Units
The direction of that field can be found using a right-hand rule. Place the thumb in the direction of the current and wrap the fingers around the wire in the direction of the magnetic field, as shown in the figure below. (i) If the current in the above figure is reversed and now points downward, what is the direction of the magnetic field? clockwise counterclockwise The equation for the strength of the magnetic field due to the current I in a long, straight wire was experimentally found to be the following. B = μ0 I2πr The proportionality constant μ0 is called the permeability of free space. μ0≡4π×10−7 T⋅m/A Calculate the magnetic field (in T) at a distance 6.0 cm away from a wire that carries a current of 0.50 A . T
One component of a magnetic field has a magnitude of 0.0285 T and points along the +x axis, while the other component has a magnitude of 0.0626 T and points along the -y axis. A particle carrying a charge of +1.98×10−5 C is moving along the +z axis at a speed of 4.76×103 m/s. (a) Find the magnitude of the net magnetic force that acts on the particle. (b) Determine the angle that the net force makes with respect to the +x axis. (a) Number Units (b) Number Units
A uniform magnetic field passes through a horizontal circular wire loop at an angle 15.1 from the normal to the plane of the loop. The magnitude of the magnetic field is 2.15 T, and the radius of the wire loop is 0.220 m. Determine the magnetic flux Φ through the loop. Φ = Wb
A rectangular coil of 100 turns and the dimensions 10 cm by 30 cm is placed in a uniform magnetic field of 0.8 T. The coil rotates such that its orientation with the field changes from 30 degrees to 60 degrees in 0.1 second. What is the magnitude of induced emf in the coil? 0.1 V 13.2 V 8.8 V 1.2 V
A free electron in a uniform magnetic field of 6.76 T flips its orientation from parallel to the magnetic field to anti-parallel. How much energy is associated with the change? eV
A circular wire loop of radius 13.2 cm carries a current of 3.89 A . It is placed so that the normal to its plane makes an angle of 37.3∘ with a uniform magnetic field of magnitude 15.9 T. (a) Calculate the magnitude of the magnetic dipole moment of the loop in amperes-square meters. (b) What is the magnitude of the torque acting on the loop? (a) Number Units (b) Number Units
SAMPLE PROBLEM 13.4 A 2000−lb car starts from rest at point 1 and moves without friction down the track shown. (a) Determine the force exerted by the track on the car at point 2, where the radius of curvature of the track is 20 ft. (b) Determine the minimum safe value of the radius of curvature at point 3.
Multiple-Concept Example 13 presents useful background for this problem. The cheetah is one of the fastest accelerating animals, for it can go from rest to 25.3 m/s in 5.19 s. If its mass is 103 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in (a) watts and (b) horsepower. (a) Number Units (b) Number Units
The figure shows a 12.0 V battery and three initially uncharged capacitors (C1 = 6.00 μF, C2 = 12.0 μF, C3 = 18.0 μF). The switch is first thrown to the left to charge capacitor 1. Then it is thrown to the right to transfer some of the charge to capacitors 2 and 3. When equilibrium is reached, what is the charge (μC) on capacitor 2?
What is the direction of the magnetic force on a negative charge that moves as shown in each of the six cases? Show me why and answers for full credits. (30pt) (a) (d) (b) (e) (c) (f)
Two tiny conducting spheres are identical and carry charges of −19.2 μC and +66.6 μC. They are separated by a distance of 2.24 cm. (a) What is the magnitude of the force that each sphere experiences? (b) The spheres are brought into contact and then separated to a distance of 2.24 cm. Determine the magnitude of the force that each sphere now experiences. (a) Number Units (b) Number Units
In the figure shown below, the vertical component of the phasor moves in simple harmonic motion. (a) Does the horizontal component also move in simple harmonic motion? (b) What is the phase difference Δϕ = ϕv − ϕh between the vertical and horizontal components?
What is the average angular velocity of a segment in units of radians per second if the initial angle was 41 degrees at time 1.25 seconds and the the final angle was 62 degrees at a time of 1.30 seconds (round your final answer to the nearest whole number)? A. 7 B. 420 C. -420 D. -7
Consider the driven LC circuit below, with inductance 9 H, capacitance 4.8 mF, and generator voltage E = 450 cos(ωt). If resonance occurs when no current passes through the voltage generator, then what is the angular frequency ω0 of the generator at resonance for this circuit? a. 151.79 radians /s b. 207.85 radians/s c. 284.60 radians /s d. 4.81 radians /s e. 0.73 radians/s
A clock pendulum oscillates at a frequency of 2.5 Hz. At t = 0, it is released from rest starting at an angle of 12∘ to the vertical. Ignoring friction, what will be the position (angle in radians) of the pendulum at (a)t = 0.25 s, (b)t = 1.60 s, and (c)t = 500 s? For pi answers, us pi/## a) Magnitude: b) Magnitude: c) Magnitude:
As you stand near a railroad track, a train passes by at a speed of 34.3 m/s while sounding its horn at a frequency of 214 Hz. What frequency fa do you hear as the train approaches you? What frequency fr do you hear while it recedes? Use 343 m/s for the speed of sound in air. fa = Hz fr = Hz
The circuit shown in the Figure has sides d1 = d2 = 0.53 m, and is placed in a uniform magnetic field that is directed into the page and decreasing at a rate of 7.8 T/s. (Assume R = 1.8 Ω and Vbat = 2.6 V). The current in the circuit is: a. 1.44 A b. 0.23 A c. 0.00 A d. 2.66 A e. 1.22 A
A 0.17-kg ball on a stick is whirled on a vertical circle at a constant speed. When the ball is at the three o'clock position, the stick's tension is 16 N. Find the tension in the stick when the ball is (a) at the twelve o'clock and (b) at the six o'clock positions. (a) T = (b) T =
At time t = 0, a ball is struck at ground level and sent over level ground. The figure here gives the magnitude p of the ball's momentum versus time t during the ball's flight ( p0 = 7.0 kg⋅m/s and p1 = 1.0 kg⋅m/s). At what initial angle is the ball launched? (Hint: Find a solution that does not require you to read the time at the low point of the plot.)
Ball A has a speed of 19.5 ft/s and Ball B has a speed of 23.5 ft/s just before the impact shown. If the balls have the same mass, and impact with a coefficient of restitution of 0.5, find the magnitude of the velocity of Ball B just after impact.
Children playing in a playground on the flat roof of a city school lose their ball to the parking lot below. One of the teachers kicks the ball back up to the children as shown in the figure below. The playground is 4.70 m above the parking lot, and the school building's vertical wall is h = 6.10 m high, forming a 1.40 m high railing around the playground. The ball is launched at an angle of θ = 53.0∘ above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (Due to the nature of this problem, do not use rounded intermediate values-including answers submitted in WebAssign-in your calculations.) (a) Find the speed (in m/s) at which the ball was launched. m/s (b) Find the vertical distance (in m) by which the ball clears the wall. m (c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands. m (d) What If? If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (Hint: You may need to use the trigonometric identity sec2(θ) = 1+tan2(θ).) ∘ above the horizontal (e) What would be the horizontal distance (in m) from the wall to the point on the roof where the ball lands in this case? m
The figure gives an overhead view of the path taken by a 0.162 kg cue ball as it bounces from a rail of a pool table. The ball's initial speed is 2.18 m/s, and the angle θ1 is 62.6∘. The bounce reverses the y component of the ball's velocity but does not alter the x component. What are (a) angle θ2 and (b) the magnitude of the change in the ball's linear momentum? (The fact that the ball rolls is irrelevant to the problem.) (a) Number Units (b) Number Units
Determine the electric potential energy for the array of three charges in the drawing, relative to its value when the charges are infinitely far away and infinitely far apart. Number Units
Two point charges, +4.40 μC and −8.40 μC, are separated by 1.70 m. What is the electric potential midway between them? Number Units
A pulley and string arrangement is used to connect two objects A and B as shown in the diagram below. Here, mA = 3.85 kg and mB = 7.95 kg. The string connecting the two objects is of negligible mass and the pulley is frictionless. The objects start from rest and move with constant acceleration. (a) What is the magnitude of the acceleration (in m/s2) of each of the objects? m/s2 (b) What is the magnitude (in N) of the tension in the string? N (c) Through what distance (in m) will the two objects move in the first two seconds of motion? m
An object is moving in the xy-plane along the path shown by the blue curve. The object moves at constant speed. Which of the diagrams shown below shows the velocity vectors of the object at the points P1 and P2? 2 1 3 4
A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below. (a) Find the work done by the force on the object as it moves from x = 0 to x = 4.00 m. J (b) Find the work done by the force on the object as it moves from x = 4.00 m to x = 10.0 m. J (c) Find the work done by the force on the object as it moves from x = 10.0 m to x = 18.0 m. J (d) If the object has a speed of 0.550 m/s at x = 0, find its speed at x = 4.00 m and its speed at x = 18.0 m. speed at x = 4.00 m m/s speed at x = 18.0 m m/s
Four identical metallic objects carry the following charges: +1.74, +6.26, −4.73, and −9.62 μC. The objects are brought simultaneously into contact, so that each touches the others. Then they are separated. (a) What is the final charge on each object? (b) How many electrons (or protons) make up the final charge on each object? (a) Number Units (b) Number Units
A 4.55 kg object is attached to a vertical rod by two strings as in the figure below. The object rotates in a horizontal circle at constant speed 4.75 m/s. (a) Find the tension in the upper string. N (b) Find the tension in the lower string. N
A woman of mass 54.8 kg is standing in an elevator. If the elevator floor pushes up on her feet with a force of 395 N, what is the acceleration of the elevator? Assume the +y-direction to be up. Enter a negative answer if the acceleration is downward and a positive answer if the acceleration is upward. m/s2
A particle of charge +5.9 μC and mass 4.4×10−8 kg is traveling perpendicular to a 1.4−T magnetic field, as the drawing shows. The speed of the particle is 64 m/s. If the angle θ shown is free to change, what is the furthest possible position where the particle's subsequent path will intersect the y axis? Number Units
A thin nonconducting rod with a uniform distribution of positive charge Q is bent into a circle of radius R (see the figure). The central perpendicular axis through the ring is a z axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at (a) z = 0 and (b) z = ∞? (c) In terms of R, at what positive value of z is that magnitude maximum? (d) If R = 2.00 cm and Q = 4.02 μC, what is the maximum magnitude? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A circular coil that has N = 150 turns and a radius of r = 12.0 cm lies in a magnetic field that has a magnitude of B0 = 0.0730 T directed perpendicular to the plane of the coil. What is the magnitude of the magnetic flux ΦB through the coil? ΦB = T⋅m2 The magnetic field through the coil is increased steadily to 0.135 T over a time interval of 0.585 s. What is the magnitude of the emf induced in the coil during the time interval? TOOLS ×10y
A 1.1 kg mass is pulled by a constant tension 18.3 N along a rough surface with coefficient of friction 0.3. The mass is then pulled by the same magnitude tension, along the same surface, but the tension is directed at an angle of 21.5 deg above horizontal. What is the ratio of the magnitudes of the accelerations between these two scenarios aθ/aflat? (please provide your answer to 2 decimal places)
(II) A wire is formed into the shape of two half circles connected by equal-length straight sections as shown in Fig. 28-48. A current I flows in the circuit clockwise as shown. Determine (a) the magnitude and direction of the magnetic field at the center, C, and (b) the magnetic dipole moment of the circuit. Figure 28-48
As shown in the figure, a conducting rod with a linear mass density of 0.0363 kg/m is suspended by two flexible wires of negligible mass in a uniform magnetic field directed out of the page. A power supply is used to send a current through the rod such that the tension in the support wires is zero. (a) If the magnitude of the magnetic field is 3.70 T, determine the current in the conducting rod. A (b) Determine the direction of the current in the conducting rod. to the left to the right
Two long, straight wires are separated by 0.120 m. The wires carry currents of 11 A in opposite directions, as the drawing indicates. Find the magnitude of the net magnetic field at the points labeled (a) A and (b) B. (a) Number Units (b) Number Units
Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.248 m . In a vacuum, each object carries a different charge, and they attract each other with a force of 1.32 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object, the answer to part (a) being the one with the greater (and positive) value? (a) Number Units (b) Number Units
A 2500−kg rocket is released from a space station. As it burns fuel, the rocket's mass decreases and its velocity increases. Let v(m) be the velocity (in meters per second) as a function of mass m. Find the velocity when m = 1444 kg if dv/dm = −40 m −1/2. Assume that v(2500) = 0. (Use symbolic notation and fractions where needed.) v(1444) = m/s
The rough inclined plane is rotating about a vertical axis at a constant rate Ω. The small block of mass 0.1 kg rests on the inclined plane. The coefficient of static friction between the block and the plane is μ = 1 /2. If θ = 45∘ and d = 100 mm, determine the minimum and maximum values of Ω to keep zero relative motion between the block and the inclined plane.
A 13 g wire of length L = 62 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.440 T (as shown in the figure). What are the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads? (5 points)
The figure shows a cross section across a long cylindrical conductor of radius a = 2.96 cm carrying uniform current 25.0 A. What is the magnitude of the current's magnetic field at radial distance (a) 0, (b) 1.69 cm, (c) 2.96 cm (wire's surface), (d) 4.84 cm? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Two particles, each of mass 3.15×10−4 kg and speed 6.17 m/s, travel in opposite directions along parallel lines separated by 4.90 cm. (a) What is the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines? (b) Is the value different for a different location of the point? If the direction of either particle is reversed, what are the answers for (c) part (a) and (d) part (b)? (a) Number Units (b) (c) Number Units (d)
A 55.0−kg box is being pushed a distance of 7.84 m across the floor by a force P→ whose magnitude is 180 N. The force P→ is parallel to the displacement of the box. The coefficient of kinetic friction is 0.209. Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force. (a) Wp = (b) Wf = (c) Wmg = (d) WN =
A small sphere of mass m = 7.30 g and charge q1 = 28.7 nC is attached to the end of a string and hangs vertically as in the figure. A second charge of equal mass and charge q2 = −58.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in the figure. (a) Find the tension in the string. N (b) If the string can withstand a maximum tension of 0.180 N , what is the smallest value d can have before the string breaks? cm
In the figure, an electron moves at speed v = 58.8 m/s along an x axis through uniform electric and magnetic fields without accelerating. The magnetic field B→ is directed into the page and has magnitude 4.88 T. In unit-vector notation, what is the electric field? Number Units
In the figure, an electron moves at speed v = 58.8 m/s along an x axis through uniform electric and magnetic fields without accelerating. The magnetic field B→ is directed into the page and has magnitude 4.88 T. In unit-vector notation, what is the electric field? Number Units
The figure below shows two current-carrying loops with I1 = 4.40 A clockwise and I2 = 8.60 A counterclockwise, placed with their centers at the origin of the xy plane. (a) If r1 = 12.5 cm and r2 = 18.5 cm, what are the magnitude and direction of the magnetic field due to the two loops at the origin? magnitude T direction (b) If r1 is held constant at 12.5 cm, what would r2 have to be for the magnetic field at the origin to be 0? cm
The figure below shows a rod of length L = 14.0 cm that is forced to move at constant speed v = 2.00 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.500 Ω; the rest of the loop has negligible resistance. A current i = 110 A through the long straight wire at distance a = 10.0 mm from the loop sets up a (nonuniform) magnetic field through the loop. (a) Find the emf induced in the loop. V (b) Find the current induced in the loop. A (c) At what rate is thermal energy generated in the rod? W (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? N (e) At what rate does this force do work on the rod? W
Four identical metallic objects carry the following charges: +1.56, +6.21, −4.88, and −9.51 μC. The objects are brought simultaneously into contact, so that each touches the others. Then they are separated. (a) What is the final charge on each object? (b) How many electrons (or protons) make up the final charge on each object? (a) Number Units (b) Number Units
accelerate toward the positive plate. (a) Which charge will reach the plate first? the proton the electron They will both reach the plate at the same time. If tp and te are the times taken for the proton and electron to reach the plate, calculate the ratio tp te. tp te = (b) Which charge hits the plate moving the fastest? the proton the electron They both reach the plate at the same speed. If vp and ve are the speeds of the proton and electron as they hit the plate, calculate the ratio vp ve. vp ve =
There are Z protons in the nucleus of an atom, where Z is the atomic number of the element. An α particle carries a charge of +2e. In a scattering experiment, an α particle, heading directly toward a nucleus, will come to a halt when all the particle's kinetic energy is converted to electric potential energy. In such a situation, how close will an α particle with a kinetic energy of 6.40×10−13 J come to a nucleus with atomic number Z = 68? Number Units
Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.247 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 1.51 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object, the answer to part (a) being the one with the greater (and positive) value? (a) Number Units (b) Number Units
The figure shows a rod of length L = 11.7 cm that is forced to move at constant speed v = 5.31 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.340 Ω; the rest of the loop has negligible resistance. A current i = 135 A through the long straight wire at distance a = 12.5 mm from the loop sets up a (nonuniform) magnetic field throughout loop. Find the (a) magnitude of the emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
from the center is of magnitude 241 N/C and points radially outward. From this information, find the following. (Include the sign of the charge in your answer.) (a) the charge on the insulating sphere C (b) the net charge on the hollow conducting sphere C (c) the charge on the inner surface of the hollow conducting sphere c (d) the charge on the outer surface of the hollow conducting sphere c
Review Conceptual Example 5 as background for this problem. Suppose some nucleus undergoes α decay, releasing 5.7 MeV of energy. If the daughter product of this reaction is 92 236 X (atomic mass = 236.04556), it will recoil away as the α particle leaves. Determine (a) the energy of the daughter product and (b) the energy of the α particle (atomic mass = 4.002603 u). Assume that the energy of each particle is kinetic energy, and ignore any other small amounts of energy that might be carried away by other emissions. In addition, ignore relativistic effects. Before decay α particle After decay (a) Number Units (b) Number Units
A 9.89 g wire of length 76.6 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.596 T (see the figure). What is the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads? (a) Number Units (b)
The figure below is a cross-sectional view of a coaxial cable- The center conductor is surrounded by rubber layer; an outer conductor; and another rubber layer: In a particular application, the current in the inner conductor is 1.06 A out of the page and the current in the outer conductor is I2 = 2.80 A into the page. Assuming the distance d = 1.00 mm, answer the following. (a) Determine the magnitude and direction of the magnetic field at point a. magnitude μT direction (b) Determine the magnitude and direction of the magnetic field at point b. magnitude μT direction
Water flowing through a garden hose of diameter 2.71 cm fills a 20.0−L bucket in 1.45 min. (a) What is the speed of the water leaving the end of the hose? m/s (b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle? m/s
A jet airplane in level flight has a mass of 8.67×104 kg, and the two wings have an estimated total area of 95.0 m2. (a) What is the pressure difference between the lower and upper surfaces of the wings? Pa (b) If the speed of air under the wings is 235 m/s, what is the speed of the air over the wings? Assume air has a density of 1.29 kg/m3. m/s (c) Explain why all aircraft have a "ceiling," a maximum operational altitude.
In the figure below, a long circular pipe with outside radius R = 2.83 cm carries a (uniformly distributed) current i = 10.2 mA into the page. A wire runs parallel to the pipe at a distance of 3.00 R from center to center. Find the (a) magnitude and (b) direction (into or out of the page) of the current in the wire such that the ratio of the magnitude of the net magnetic field at point P to the magnitude of the net magnetic field at the center of the pipe is 1.03, but it has the opposite direction. (a) Number Units (b)
There are Z protons in the nucleus of an atom, where Z is the atomic number of the element. An α particle carries a charge of +2e. In a scattering experiment, an α particle, heading directly toward a nucleus, will come to a halt when all the particle's kinetic energy is converted to electric potential energy. In such a situation, how close will an α particle with a kinetic energy of 7.00×10−13 J come to a nucleus with atomic number Z = 58? Number Units
The x, y, and z components of a magnetic field are Bx = 0.13 T, By = 0.19 T, and Bz = 0.15 T. A 29-cm wire is oriented along the z axis and carries a current of 3.6 A. What is the magnitude of the magnetic force that acts on this wire?
The Force due to Tension 2 is 350 N. The angle θ is 75 degrees. The weight of the box is 500. Find the Force due to Tension 1 and the Force due to Tension 3 in the diagram below. (Answer: 155 N, 40 N) a) What object are you summing forces on? b) What forces are acting on that object and in what direction?
A 15.0-g conducting rod of length 1.30 m is free to slide downward between two vertical rails without friction. The ends of the rod maintain electrical contact with the rails. The rails are connected to a 7.20−Ω resistor, and the entire apparatus is placed in a 0.540−T uniform magnetic field. Ignore the resistance of the rod and rails. What is the terminal velocity of the rod? m/s
A uniformly charged solid sphere with a radius of 0.6 m and net electric charge of 450 nC is rotating with angular speed of 3 rad/s. The axis of rotation is indicated by the dashed line. The magnitude of the constant external magnetic field has a magnitude of 7 mT. What is the magnitude of dipole contribution to the net torque (in pNm) exerted on the sphere due to its interaction with the external magnetic field if θ = 60∘?
In the figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 20 cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3 , and each wire carries 23 A. What is the magnitude of the net magnetic field at the square's center? Number Units
A loop of wire is dropped and allowed to fall between the poles of a horseshoe magnet, as shown in the figure. Problem 2 (a) Determine the direction of the induced current in the loop when the loop is ABOVE the magnet. Your work must include the original magnetic field, the induced magnetic field and the induced current. original magnetic field direction inside the loop: While the loop falls, the original magnetic flux inside the loop [ select] . Induced magnetic field direction inside the loop: [Select] Induced current in the loop (viewed in the figure): [Select] (b) Determine the direction of the induced current in the loop when the loop is BELOW the magnet. Your work must include the original magnetic field, the induced magnetic field and the induced current. original magnetic field direction inside the loop: [ Select ] While the loop falls, the original magnetic flux inside the loop [ Select ] Induced magnetic field direction inside the loop: [ select ] . Induced current in the loop (viewed in the figure): [ Select ]
Five particles follow the paths shown in the figure as they pass through a magnetic field B, which points out of the page. What can you conclude about the charge of each particle? Path 1 Path 2 Path 3 Path 4 Path 5
The square loop shown in the figure below is coplanar with a long, straight wire that carries an electric current I(t) = 5 cos(2π×104t) The loop has a resistance of 5 Ω. Determine the electric current in the loop as a function of time.
Problem 2. Two current loops have their center at the origin. A loop with a radius of 5 cm lies in the z = 0 plane. A loop with a diameter of 10 cm lies in the x = 0 plane. The first coil has a current of 12 A and the second coil (x = 0 plane) has a current of -12 A . What is the magnetic field intensity at the origin? You must show your work to get credit for the problem. Simply writing the correct answer without showing your work will result in a zero for the problem.
Based on the velocity vs time graph shown, the object is speeding up at time = seconds. 1.5 2.5 0.5 none of the listed times are correct 3.5
A circular wire loop of radius 21.2 cm carries a current of 3.13 A. It is placed so that the normal to its plane makes an angle of 54.3∘ with a uniform magnetic field of magnitude 11.6 T. (a) Calculate the magnitude of the magnetic dipole moment of the loop in amperes-square meters. (b) What is the magnitude of the torque acting on the loop? (a) Number Units (b) Number Units
The conducting bar illustrated in the figure moves on two frictionless, parallel rails in the presence of a uniform magnetic field directed into the page. The bar has mass m, and its length is ℓ. The bar is given an initial velocity v→i to the right and is released at t = 0. (A) Using Newton's laws, find the speed of the bar as a function of time after it is released.
Consider the following. (a) Find the resultant magnetic force exerted by the long wire on the square current loop in the figure below if I1 = 7.60 A and I2 = 4.24 A. The edge length of the square is 22.0 cm, and the distance from the long wire to the closest edge of the loop is 5.45 cm. magnitude direction (b) Find the magnetic torque on the current loop. magnitude direction
The line integral of the magnetic field around this boundary is equal to 5π×10−13 Tm. If I1 = 5 μA and I3 = 2 μA, what is the magnitude of the I2 electric current (in μA)? Assume the system is in vacuum.
A block that has a mass of m = 4.5 kg rests on a horizontal plane. The coefficient of static friction, Ms, is 0.25. A horizontal force, F, is applied to the block, and it is just big enough to get the block to begin moving. a) Write an expression for the sum of the forces in the x-direction using the variables from the above Free Body Diagram b) Given the coordinate system specified in the problem statement, write an expression for the sum of the forces in the y-direction. c) Write an expression to show the relationship between the maximum friction force, Ff, and the normal force, FN. d) Calculate the magnitude of F, in INewtons, if Ff is at its maximum
A person whose mass is m = 81.0 kg steps on a mechanical bathroom scale that rests on a slope inclined at an angle α = 14.3∘ above the horizontal. What mass m′ does the scale read? m′ = kg
A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A , directly toward plate B, with an initial speed of v0 = 2.0×107 m/s. What is the speed of the electron as it strikes plate B ? (e = 1.6×10−19 C, melectron = 9.11×10−31 kg) A) 1.8×107 m/s B) 2.1×107 m/s C) 2.4×107 m/s D) 1.2×107 m/s E) 1.5×107 m/s
As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.536)v after passing through the target. (a) Before collision (b) After collision The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEbBC ] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V = v M = m
There is a configuration of 9 charges. 8 of them are positive and one is negative. Every charge has a magnitude of 1 μC (one microCoulomb). One positive charge is placed in the center of a circle with radius . 05 m , while the other 8 are evenly distributed around the circumference of the circle (45 degrees from each other) with the negative charge placed at the top (see the diagram below). What is the magnitude of the net force on the charge in the middle in Newtons? (Hint: do not calculate the force from every single charge, consider the directions and relative magnitudes)
Find the x and y coordinates of the center of mass for the object of uniform linear mass density shown below. A 1L x1L section has been removed from the rectangle. x = 1.425L and y = 0.85L x = 1.65L and y = 0.75L x = 1.425L and y = 0.65L x = 1.65L and y = 0.85L x = 1.425L and y = 0.75L
The drawing shows three identical rods (A, B, and C) moving in different planes. A constant magnetic field of magnitude 0.67 T is directed along the +y axis. The length of each rod is L = 1.6 m, and the speeds are the same, vA = vB = vC = 3.7 m/s. Find the magnitude of the motional emf for the rods (a) A, (b) B, and (c) C. (a) Number Units (b) Number Units (c) Number Units
A magnetic field has a magnitude of 0.0791 T and is uniform over a circular surface whose radius is 0.297 m. The field is oriented at an angle of ϕ = 29.1∘ with respect to the normal to the surface. What is the magnetic flux through the surface? Number Units
Two traveling waves, y1(x, t) and y2(x, t), are generated on the same taut string. Individually, the two traveling waves can be described by the two equations y1(x, t) = (1.73 cm)sin[k1 x+(0.173 rad/s)t+ϕ1]y2(x, t) = (6.03 cm)sin[k2 x−(7.76 rad/s)t+ϕ2] where k1 and k2 are the wave numbers and ϕ1 and ϕ2 are the phase angles. If both of the traveling waves exist on the string at the same time, what is the maximum positive displacement Δy that a point on the string can ever have? Δy = cm What are the smallest positive values of the unknown phase constants ϕ1 and ϕ2 (in radians) such that the maximum displacement occurs at the origin (x = 0) at time t = 2.01 s? ϕ1 = rad ϕ2 = rad
The 3.6 kg box in this situation starts from rest and travels 1.2 m from the bottom to the top of the inclined plane in 2.4 seconds. Solve for the force of kinetic friction between the box and the inclined plane. 3.0 N 2.4 N 9.9 N 8.5 N 6.0 N
A 120.0-V motor draws a current of 7.96 A when running at normal speed. The resistance of the armature wire is 0.612 Ω. (a) Determine the back emf generated by the motor. (b) What is the current at the instant when the motor is just turned on and has not begun to rotate? (c) What series resistance must be added to limit the starting current to 15.0 A? (a) Number Units (b) Number Units (c) Number Units
A flat, circular, steel loop of radius 55 cm is at rest in a uniform magnetic field, as shown in an edge-on view in the figure. The magnetic field changes from 0 to 1.5×10−3 T in a time interval of 0.02 sec. In this time, what is the average emf induced around the loop? 61.7 mV 35.6 mV 24.7 mV 16.5 mV 41.3 mV
A uniform magnetic field passes through a horizontal circular wire loop at an angle 15.1∘ from the normal to the plane of the loop. The magnitude of the magnetic field is 4.55 T, and the radius of the wire loop is 0.280 m. Determine the magnetic flux Φ through the loop. Φ = Wb
Magnetic Field vs. Time The magnetic field through a single loop of wire 18.7 cm in radius and of 8.55 Ω resistance, changes with time as shown in the figure above. The uniform magnetic field is perpendicular to the plane of the loop. Calculate the magnitude of the EMF in the loop as a function of time in each of the following time intervals: (a) t = 0 to t = 2.0 s
A basketball player shoots when she is 16 ft from the backboard. Given the ball has an initial velocity v0 at an angle of 30∘ with the horizontal. Determine the value of v0 when d is equal to 26 in. The value of v0 is ft/s.
Two ice skaters, whose masses are 55 kg and 85 kg, hold hands and rotate about a vertical axis that passes between them, making one revolution in 2.5 s. Their centers of mass are separated by 1.7 m and their center of mass is stationary. Model each skater as a point particle and find (a) the angular momentum of the system about their center of mass and (b) the total kinetic energy of the system. 0.12 kJ. s and 0.05 kJ 0.24 kJ. s and 0.21 kJ 0.14 kJ. s and 0.31 kJ 0.24 kJ. s and 0.31 kJ
For the real or imaginary nucleus of 88 221 X, find (a) the net electrical charge of the nucleus, (b) the number of neutrons, (c) the number of nucleons, (d) the approximate radius of the nucleus, and (e) the nuclear density. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
(a) Determine the net electric field at point P if the particles' respective charges are q1 = −3.00 nC, q2 = 4.00 nC and, q3 = 9.00 nC and their distances from the point are as indicated. Your answer must be in unit vector notation consistent with your coordinate system. (b) Determine the magnitude and the direction of the acceleration that an electron released from rest at P would initially experience.
Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 4 ft/s. How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q? (Hint: There are a few different ways to solve this, but note that side AP and side BP are changing at the same speed) (Round your answer to two decimal places) (Note the question asks "How FAST. . . " so enter your answer as a positive number even though the distance from B to Q is getting smaller) ft/s
The figure below shows a loop of wire of mass m = 0.0251 kg, width L = 0.0537 m, and resistance R = 0.494 Ω dropping out of a region of constant magnetic field of magnitude B = 1.47 T pointing into the page. As long as the top of the loop is in the magnetic field, the equation describing the speed of the loop v is given by mdvdt + vL2 B2 R = mg. Replacing the speed by the current i, this equation has the same form as that for a series RL circuit. What is the speed of the loop after t = 3.58 s?
Consider the given circuit where Vx = 13.50 V. Determine the current labeled i in the given circuit after first transforming the circuit such that it contains only resistors and voltage sources. (Round the final answer to three decimal places.) (Include a minus sign if necessary.) The value of current i is nA.
In the figure, a particle moves along a circle in a region of uniform magnetic field of magnitude B = 3.5 mT. The particle is either a proton or an electron (you must decide which). It experiences a magnetic force of magnitude 3.4×10−15 N. What are (a) the particle's speed, (b) the radius of the circle, and (c) the period of the motion?
A cube of edge length ℓ = 1.00 cm is positioned as shown in the figure below. A uniform magnetic field given by B→ = (4.5 i^ + 4.0 j^ + 3.0 k^)T exists throughout the region. (a) Calculate the magnetic flux through the shaded face. mWb (b) What is the total flux through the six faces? mWb
A magnetic field directed into the page changes with time according to B = 0.0530t2 + 1.40, where B is in teslas and t is in seconds. The field has a circular cross section of radius R = 2.50 cm (see figure below). (a) When t = 2.50 s and r2 = 0.0200 m, what is the magnitude of the electric field at point P2? N/C (b) When t = 2.50 s and r2 = 0.0200 m, what is the direction of the electric field at point P2? into the page perpendicular to r2 and counterclockwise perpendicular to r2 and clockwise out of the page
The girl skis with an initial speed v = 22 m/s. She will land on the slope at a horizontal x-distance (not distance along slope) of meter.
Which describes the image distance and object distance for a flat (plane) mirror? The image distance is greater. The image distance is smaller. The distances are equal.
Which describes the focus of a concave spherical mirror? The focus is real. The focus is virtual. The focus can be real or virtual, depending on the object distance.
The lateral magnification of an object by a lens is negative. Which is true? The image must be a virtual image. The image must be a real image. The image could be either a real or virtual image.
Which is true about the overall magnification of a compound microscope? It is the sum of the lateral magnifications of the objective and the eyepiece. It is the product of the angular magnifications of the objective and the eyepiece. It is the sum of the angular magnification of the objective and the lateral magnification of the eyepiece. It is the sum of the angular magnifications of the objective and the eyepiece. It is the product of the lateral magnifications of the objective and the eyepiece. It is the sum of the lateral magnification of the objective and the angular magnification of the eyepiece. It is the product of the angular magnification of the objective and the lateral magnification of the eyepiece. It is the product of the lateral magnification of the objective and the angular magnification of the eyepiece.
Which describes light as it passes from air into glass? Both the wavelength and the frequency increase. Both the wavelength and the frequency remain the same. The wavelength decreases but the frequency remains the same. The frequency increases but the wavelength remains the same. The wavelength increases but the frequency remains the same. Both the wavelength and the frequency decrease. The frequency decreases but the wavelength remains the same.
What is the value of φ for the first minimum to either side of the central maximum in the double-slit interference pattern? 0.5π 1.0π 1.5π 2.0π 2.5π 3.0π 3.5π 4.0π 4.5π 5.0π
If we move mirror M2 in a Michelson interferometer and the fringe pattern shifts by 0.50 fringe, how far did we move the mirror? 0 wavelength 0.25 wavelength 0.50 wavelength 0.75 wavelength 1.00 wavelength 2.00 wavelengths
To determine the type of interference at a point on the viewing screen, which is done? We pair the ray from the top of one zone with the ray from the top of the adjacent zone and then determine their path length difference. We pair the ray from the top of one zone with the ray from the bottom of the adjacent zone and then determine their difference in angle to the point on the screen. We pair the ray from the top of one zone with the ray from the bottom of the adjacent zone and then determine their path length difference. We pair the ray from the top of one zone with the ray from the top of the adjacent zone and then determine their difference in angle to the point on the screen.
Which is true? Two objects are resolvable if the angle between them is smaller than that given by Rayleigh's criterion. Two objects are resolvable if the angle between them is equal to that given by Rayleigh's criterion. Two objects are resolvable if the angle between them is greater than that given by Rayleigh's criterion.
Which is true about a grating with a given slit separation, illuminated by a given beam of light? Decreasing the number of slits increases the half-width of the lines, increasing the overlap of the lines. Decreasing the number of slits increases the half-width of the lines, decreasing the overlap of the lines. Decreasing the number of slits decreases the half-width of the lines, increasing the overlap of the lines. Decreasing the number of slits decreases the half-width of the lines, decreasing the overlap of the lines.
An image is projected from a converging lens of focal length 100 cm onto a screen 3.0 m behind the lens. Where is the object? 150 cm behind the lens 3.1 cm behind the lens 150 cm in front of the lens None of the choices are correct. 3.1 cm in front of the lens
Consider a single-slit diffraction pattern caused by a slit of width a. There is a minimum at sinθ equal to slightly more than λ/a exactly λ/a slightly less than λ/a very nearly 2λ/a exactly λ/2a
A double-slit pattern is obtained using monochromatic light. Consider the following five possible changes in conditions: 1.) decrease the wavelength 2.) increase the wavelength 3.) increase the width of each slit 4.) increase the separation between the slits 5.) decrease the separation between the slits Which of the above would increase the spacing of the interference fringes? 3 only 5 only 2 and 5 only 1 and 5 only 1 and 3 only
Light of wavelength 720. nm is incident upon a single slit with width 0.0440 mm . The figure shows the pattern observed on a screen 2.00 m from the slits. What is the distance s? mm
A blue laser is incident on a pair of double slits, creating an interference pattern a distance of 4.0 m away. If you wish to make the spacing of the spots in the pattern closer together, Decrease the distance between the two slits. Increase the distance between the two slits. Replace the blue laser with a violet laser. Replace the blue laser with a red laser.
The object-lens distance for a certain converging lens is 300 mm. The image is three times the size of the object. To make the image five times the size of the object, the object-lens distance must be changed to 450 mm 405 mm 540 mm 720 mm 270 mm
In the figure, a light wave along ray r1 reflects once from a mirror and a light wave along ray r2 reflects twice from that same mirror and once from a tiny mirror at distance L from the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength 620. nm and are initially exactly out of phase. What is the smallest value of L that results in the final waves being exactly in phase? 465 nm 310. nm 775 nm 620. nm 155 nm
In the figure, a light wave along ray r1 reflects once from a mirror and a light wave along ray r2 reflects twice from that same mirror and once from a tiny mirror at distance L from the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength 480. nm and are initially exactly out of phase. What is the smallest value of L that results in the final waves being exactly in phase? 600. nm 120. nm 240. nm 480. nm 360. nm
It is possible for a dark fringe for two different wavelengths to occur at the same angle. Consider light of wavelength 600. nm and 300 nm. They both have a dark fringe at 1.05 mrad. For what minimum slit width is this possible (in mm)? mm
The figure below shows the graph of intensity as a function of angular position for a double-slit diffraction experiment. The diffraction pattern was created by passing light of wavelength 468 nm through two parallel slits. What is the separation of the slits that corresponds to such an intensity distribution (in μm)? μm
An image is projected from a converging lens of focal length 80 cm onto a screen 4.0 m behind the lens. Where is the object? 100 cm behind the lens None of the choices are correct. 4.2 cm in front of the lens 100 cm in front of the lens 4.2 cm behind the lens
Reflection by thin layers. In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) The waves of rays r1 and r2 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). The table below provides the indexes of refraction n1, n2, and n3, the type of interference, and the wavelength λ in nanometers of the light as measured in air. Give the third least thickness L. n1 n2 n3 Type L λ 1.271.70 1.43 max 3rd 390
Reflection by thin layers. In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) The waves of rays r1 and r2 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). The table below provides the indexes of refraction n1, n2, and n3, the type of interference, and the thin layer thickness L in nanometers. Give the wavelength that is in the visible range. n1 n2 n3 Type L λ 1.33 1.79 1.40 max 362
Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +19 centimeters, the type of mirror is convex, and then the distance between the focal point and the mirror is 14 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side. (a) Number Units (b) Number Units (c) Number Units (d) (e) (f)
More mirrors. Object O stands on the central axis of a spherical or plane mirror. For this situation (see the table below, all distances are in centimeters), find (a) the type of mirror, (b) the radius of curvature r (nonzero number or 0 if infinity), (c) the object distance p, (d) the magnification (including sign), whether (e) the image is real or virtual, (f) inverted or noninverted from O, and (g) on the same side of the mirror as object O or on the opposite side.
A thin flake of transparent material (n = 1.40) is used to cover one slit of a double-slit interference arrangement. The central point on the screen is now occupied by what had been the 3 th bright side fringe (m = 3). If λ = 668 nm, what is the thickness of the flake in meters? Number Units
A disabled tanker leaks kerosene (n = 1.20) into the Persian Gulf, creating a large slick on top of the water (n = 1.30). (a) If you are looking straight down from an airplane, while the Sun is overhead, at a region of the slick where its thickness is 445 nm , for which wavelength(s) of visible light is the reflection brightest because of constructive interference? (b) If you are scuba diving directly under this same region of the slick, for which wavelength(s) of visible light is the transmitted intensity strongest? (a) Number Units (b) Number Units
(a) What is the angular separation of two stars if their images are barely resolved by a refracting telescope with a lens diameter of 100 cm and a focal length of 15 m. Assume λ = 550 nm. (b) Find the distance between these barely resolved stars if each of them is 8.9 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern in meters, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens "errors." (a) Number Units (b) Number Units (c) Number Units
Assume that the limits of the visible spectrum are arbitrarily chosen as 430 and 660 nm. Calculate the number of rulings per millimeter of a grating that will spread the first-order spectrum through an angle of 28.0∘. Number Units
Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +23 centimeters, the type of mirror is convex, and then the distance between the focal point and the mirror is 42 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side. (a) Number Units (b) Number Units (c) Number Units (d) (e) (f)