(a) A 500 g block is shot on the surface in FIGURE 3 with an initial speed of 0.5 ms−1. How far will it go if the coefficient of friction between it and the surface is 0.150? [3 marks] (b) A 0.25 hp motor is used to lift a load at the rate of 5.0 cms−1. Determine the mass of the load at this constant speed? [1 hp = 746 W] [3 marks] (c) At sea level, a nitrogen molecule in the air has kinetic energy of 6.2×10−21 J. Its mass is 4.7×10−26 kg. If the molecule could shoot straight up without striking other air molecules, how high would it rise? [2 marks]
A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 4.75 km/s in the +x direction experiences a force of 1.50×10−16 N in the +z direction, and an electron moving at 8.50 km/s in the +y direction experiences a force of 2.25×10−16 N in the +z direction. What is the direction of the magnetic field? (The direction is an angle measured counterclockwise from the positive x axis to the nearest 0.1 degrees) 50.0∘ 75.2∘ 94.8∘ 159.6∘ 230.0∘ 255.2∘ 274.8∘ 339.6∘
At a distance of 5.1 cm from a long straight wire carrying current/ the magnetic field is 2.5 mT. A 1.0 cm diameter loop carries the same current/ as the long straight wire. What is the strength of the magnetic field at the center of the loop? 78 μT 79 μT 80 μT 78 mT 79 mT 80 mT none of the above
Two parallel, very long wires 1 and 2 are separated by a distance r and carry currents of I1 = 3.5 A and I2 = 2.5 A. The magnitude of the force on a 4 m section of wire 2 due to the magnetic field produced by the current in wire 1 when the currents flow in opposite directions is F = 5.0×10−4 N, calculate the distance r. a. 4 m b. 28 cm c. 14 mm d. 14 cm e. None of the above.
Consider the picture bellow: a positively charged particle moving through an electric and magnetic field, with the E field pointing out of the page. Out of the four possible directions for the particle's velocity, which one could lead to zero net force? (4) (2) (1) (3)
A block of mass 500 g is attached to a spring of spring constant 80 N/m as shown below. The other end of the spring is attached to a support while the mass rests on a rough surface with a coefficient of friction of 0.20 that is inclined at angle of 30∘. The block is pushed along the surface till the spring compresses by 10 cm and is then released from rest. (a) How much potential energy was stored in the block-spring-support system when the block was just released? (b) Determine the speed of the block when it crosses the point when the spring is neither compressed nor stretched. (c) Determine the position of the block where it just comes to rest on its way up the incline. (15 points)
Figure 5.13 shows the velocity of a particle, in cm/sec, along a number line for time −3 ≤ t ≤ 3. (a) Describe the motion in words: Is the particle changing direction or always moving in the same direction? Is the particle speeding up or slowing down? (b) Make over and underestimates of the distance traveled for −3 ≤ t ≤ 3. Figure 5.13
Shown in the figure below is a rectangle of wire immersed in a magnetic field. The rectangle has length L = 4 meters, width w = 2 meters, and a resistance of R = 8.38 Ω. The magnetic field varies with time according to the equation: B(t) = 5t2 + 3t4 As a result of the varying field, a voltage and current will be established in the loop. Answer all of the following: What is the FORMULA for the rate of change of magnetic field with time, dB/dt = What is the FORMULA for the rate of change of magnetic flux with time, dΦB/dt = What is the voltage in the circuit at t = 1.5 seconds? Volts What is the current in the circuit at this same time? Amps NOTE: Make all formulas POSITIVE (field and flux). Make all values POSITIVE (voltage and current). Format your equations as atn + btm where a, b, n, m are numerical values. Example: 12t2 + 72t3
Shown in the figure below is a rectangle of wire immersed in a magnetic field. The rectangle has length L = 2 meters, width w = 2 meters, and a resistance of R = 7.02 Ω. The magnetic field varies with time according to the equation: B(t) = 5t3 + 2t4 As a result of the varying field, a voltage and current will be established in the loop. B-field into the screen Answer all of the following: What is the FORMULA for the rate of change of magnetic field with time, dB/dt = What is the FORMULA for the rate of change of magnetic flux with time, dΦB/dt = What is the voltage in the circuit at t = 1.2 seconds? Volts -What is the current in the circuit at this same time? Amps NOTE: Make all formulas POSITIVE (field and flux). Make all values POSITIVE (voltage and current). Format your equations atn + btm where a, b, n, m are numerical values. Example: 12t2 + 72t3
A right circular cone of base circle radius R and slant height L rolls without slip on the ground. The line of contact with the ground rotates about the vertical at an angular rate Ω. Find the angular velocity and angular acceleration of the cone at the instant when the line of contact coincides with the Y axis. [Hint: Angular velocities can be added as they are vectors]
A Nichrome (resistive) wire has the shape of two quarter-circles of radius a = 3.94 cm and b = 16.1 cm, connected by straight sections, which lie on the radii of the arcs, as shown. The wire carries conventional current I = 8.68 A in the direction shown. What is the net magnetic field, in microTesla, at Point C due to the wire loop. Use a negative sign if directed into the page and a positive sign if directed out of the page. Add your answer
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
A solenoid has a length l = 17.96 cm, a radius a = 1.98 cm, and 1561 turns. The solenoid has a net resistance Rsol = 120.5 Ω. A circular loop with radius b = 3.65 cm is placed around the solenoid, such that it lies in a plane whose normal is aligned with the solenoid axis, and the center of the outer loop lies on the solenoid axis. The outer loop has a resistance Ro = 1908.5 Ω. At a time t = 0 s, the solenoid is connected to a battery that supplies a potential E = 37.48 V. At a time t = 2.58 μs, what current flows through the outer loop? A
The figure below shows a circular region of radius R = 0.100 m with a time-varying magnetic field of magnitude B = bt which points into the page. If b = 3.11 T/s, what is the magnitude of the electric field at r = 0.606 m. V/m
In the figure, a 100-turn coil of radius 3.3 cm and resistance 4.7 Ω is coaxial with a solenoid of 240 turns /cm and diameter 4.7 cm. The solenoid current drops from 1.2 A to zero in time interval Δt = 22 ms. What current is induced in amperes in the coil during Δt? Number Units
Scientists design a new particle accelerator in which protons (mass 1.7×10−27 kg) follow a circular trajectory given by r→ = ccos(kt2)ı^ + csin(kt2)ȷ^, where c = 4.0 m and k = 8.0×104 rad/s2 are constants and t is the elapsed time. Part A What is the radius of the circle? Express your answer with the appropriate units. View Available Hint(s) R = Value Units Submit
The conducting rod ab shown in (Figure 1) makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field 0.800 T, perpendicular to the plane of the figure Figure 1 of 1 Part A Find the magnitude of the emt induced in the rod when it is moving toward the right with a speed 7.50 m/s. Express your answer in volts. Submit Request Answer Part B In what direction does the current flow in the rod? clockwise counterclockwise Part C If the resistance of the circuit abdc is 1.50 Ω (assumed to be constant), find the magnitude of the force required to keep the rod moving to the right with a constant speed of 7.50 m/s. You can ignore friction. Express your answer in newtons. Part D Find the direction of the force required to keep the rod moving to the right with a constant speed of 7.50 m/s. upward downward to the right to the left Submit Request Answer Part E Compare the rate at which mechanical work is done by the force (Fv) with the rate at which thermal energy is developed in the circuit (I2R). equal nonequal
Two coils are at fixed locations. When the magnetic flux through coil 1 is 51.2 mWb, the current in coil 2 is 67.8 mA. What rate of change of current in coil 2 will generate an emf of +15.0 mV in coil 1? Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answer units
The critical angle for total internal reflection at a liquid- air interface is 35.0∘. If a ray of light traveling in air has an angle of incidence at the interface of 54.2∘, what angle does the refracted ray in the liquid make with the normal? 33.2∘ 28.2∘ 27.7∘ 22.8∘ Answer not given
The figure shows a square loop of wire in a uniform magnetic field. The loop is a square of side length 20 cm. If the field strength changes from 0.30 to 0.10 T in 50 ms, what is the induced emf in the loop? 0 V 0.08 V 0.12 V 0.16 V 0.24 V 0.36 V
A particle with a positive charge moves in the yz-plane as shown. The magnetic field is in the positive y-direction. The magnetic force on the particle is in the positive x-direction. the negative x-direction. the positive y-direction. the negative y-direction. the positive z-direction. the negative z-direction. none of the above
A −6.00 μC point charge is moving at a constant 8.00×106 m/s in the +z-direction, relative to a reference frame. At the instant when the point charge is at the origin of this reference frame, what is the magnetic-field vector B→ it produces at the point: x = +0.300 m, y = 0, z = −0.400 m? +11.5 μT j^ −11.5 μT k^ +19.2 μT k^ −11.5 μT j^ +11.5 μT k^ −19.2 μT j^ −15.4 μT k^
Consider the circuit shown in the figure, with C1 = 5.72 μF and C2 = 7.84 μF (a) Find the equivalent capacitance (in μF) of the system. μF (b) Find the charge (in μC) on each capacitor. 5.72 μF capacitor μC 6.00 μF capacitor μC 7.84 μF capacitor μC 2.00 μF capacitor μC (c) Find the potential difference (in V) on each capacitor. 5.72 μF capacitor V 6.00 μF capacitor V 7.84 μF capacitor V 2.00 μF capacitor V (d) Find the total energy (in mJ) stored by the group. mJ