Two identical charged rings of charge Q = 1 C and radius R = 0.1 m are separated by a distance 3 R, and are fixed. A point charge of charge q = 1.0×10−9 C and mass m = 2 kg is moved by external agent from the centre of left ring to the centre of right ring. Find the work done by an external agent in joule.
Calculate, in N⋅m, the torque (moment) caused by the force of the figure, when the force F is 77.4 N, the radius R is 0.7 m, and the angle θ is 21 degrees. The gate is quarter-circular.
For the block shown above, F1 has a magnitude of 15.0 N and acts at an angle of 55.0 degrees above the horizontal, and F2 has a magnitude of 30.0 N and acts at an angle of 25.0 degrees above the horizontal. If the block has a mass of 20.0 kg, find a) the normal force exerted on the block by the ground, b) the net force in the horizontal direction, and c) the displacement of the block after 5.00 seconds if the initial speed of the block was +10.0 m/s (assume to the right is +x).
A conducting bar of length L moves with constant speed v, perpendicular to a long straight wire carrying a current I, as shown in the following figure. Show that the magnitude of the emf generated between the ends of the bar is: |ε| = μ0νI 2πrL
If the tennis player serves the ball horizontally θ = 0∘, calculate its velocity if the center of the ball clears the 36 in. net by 6 in. Also find the distance s from the net to the point where the ball hits the court surface. Neglect air resistance and the effect of ball spin
It is observed that the time for the ball to strike the ground at B is 2.5 sec, and the angle of thrown is 30 degree. Determine the speed at which the ball was thrown. a. 2.0 m/sec. b. 20.0 m/sec. c. 23.2 m/sec. d. 40.0 m/sec.
Determine the minimum initial velocity at which the ball must be kicked in order for it to just cross over the 3-m high fence. The angle of kick is 45 degree, and the ball needs 2 sec to reach the fence. a. 2.0 m/sec. b. 4.2 m/sec. c. 9.7 m/sec. d. 58.2 m/sec.
Determine the natural frequency in radians per second for the system shown. Neglect the mass and friction of the pulleys. The mass m = 5.3 kg and the spring constant k = 410 N/m. Answer: ωn = rad/s
Determine the natural frequency of the spring-mass system in both rad /sec and cycles /sec(Hz). Assume k = 32.1 lb/in., W = 90.4 lb. Answers: ωn = rad/sec fn = Hz
Two particles with mass of m are connected by a spring with the spring constant k. They freely slip without friction on the circular surface. (R > > l) (a) Find the eigenvalues of this system. (10 points) (b) Describe the mass normalized mode shape of the lowest mode. (10 points)
The natural frequency of a spring-mass system is originally 1 rad/s. The spring-mass system is connected to an inverted pendulum, with the spring attached to the midpoint of the pendulum, which has a length of 2l. Determine the mass ratio r(r = M/m) that restricts the natural frequency of the assembled system to less or equal to 2 rad/s. (Neglect the gravity, sinθ ≈ θ, cosθ ≈ 1)
A satellite has a mass of 200 kg and a radius of gyration about z axis of kz = 0.1 m, excluding the two solar panels A and B. Each solar panel (A and B ) has a mass of 15 kg and can be approximated as a thin plate. Calculate the mass moment of inertia of the entire satellite (with panels included) at two orientations of the panels (a) θ = 90∘ and (b) θ = 0∘
A small block of mass 150 g starts at rest at A, slides to B where its speed is vB = 6.4 m/s, then slides along the horizontal surface a distance 15 m before coming to rest at C. (See below. ) (a) What is the work of friction along the curved surface (in J)? (b) What is the coefficient of kinetic friction along the horizontal surface? μk =
The slider block B moves to the right with a constant velocity of vB = 65 [in/s]. Q8: Determine velocity of block A, vA [in/s]. Q9: Determine velocity of portion D of the cable, vD [in/s]. Q10: Determine relative velocity of A with respect to B, vA∣B [in/s]. Q11: Determine relative velocity of portion C of the cable with respect to portion D, vC∣D [in/s].
A bullet of mass 10 g is fired toward a 30−kg block traveling horizontally toward the bullet. The bullet takes 10 ms to pass through the block as it reverses the block's velocity from 2 m/s to the right to 3 m/s to the left with a constant acceleration. The magnitude of the force that the bullet exerts on the block is A. 30,000 N B. 15,000 N C. 2000 N D. 9000 N E. 3000 N
The figure shows four identical conducting spheres that are actually well separated from one another. Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of −32e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of 50 e), and then they are separated. The final charge on sphere W is 16e. What multiple of e gives the initial charge on sphere A? Number Units
A conductive rod, 20 cm long and 10 Ω electrical resistance, moves parallel to itself and without friction, with a speed of 5 cm/s, on a U-shaped conductor, of negligible resistance, located in the inside a magnetic field of 0.1 T. Calculate the magnetic force acting on the electrons in the bar and the electric field inside it. Find the electromotive force that appears between the ends of the rod and the intensity of the electric current that runs through the circuit and its direction. What external force must be applied to keep the rod moving? Calculate the power needed to keep the rod moving.
Consider the conducting plate shown in the figure. If V(z = 0) = 0 and V(z = 2 mm) = 50 V, determine V, E and D in the dielectric region (εr = 1.5) between the plates and ρs on the plates.
Currents I1 = 1 A and I2 = 3 A pass through two conducting parallel wires placed in the same plane, as shown in the figure. a) Explain why the resultant magnetic field is zero only at point K. [3] b) If the currents are separated by a distance d = 30 cm, what is the distance between current I1 and the point K where the resultant magnetic field is zero?
A conducting rod slides along the metal rails as shown below. The apparatus is in a uniform magnetic field of strength 0.25 T, which is directly into the page. The rod is pulled to the right at a constant speed of 5.0 m/s by a force F→. The only significant resistance in the circuit comes from the resistor shown. Find (a) emf and (b) current induced in the circuit. ε = 0.4 V, I = 0.125 A ε = 0.050 mV, I = 25 mA ε = 0.050 mV, I = 25 mA
Suppose an electric dipole P is created by the NaBr molecule, which has a bond spacing of a = 0.298 nm. The molecule is placed in a uniform electric field of 35.6 N/C (along the x-axis), with the direction of P at an angle of +47.0 deg from the positive x-axis in the xy-plane, as shown in the diagram below. Determine the torque on the dipole. (Express as a product of the Z unit vector.)
The figure shows two charged particles. Distance d is 2.00 m. What is the magnitude (in N/C ) of the net electric field at the origin? q1 = +5e q2 = −2e θ = 30.0∘ 1.57×10−9 1.12×10−8 5.47×10−8 4.00×10−9
Two point charges are fixed on the y axis: a negative point charge q1 = −29 μC at y1 = +0.23 m and a positive point charge q2 at y2 = +0.39 m. A third point charge q = +8.4 μC is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 23 N and points in the +y direction. Determine the magnitude of q2.
The figure shows a mass m = 5 kg sliding down a frictionless surface from an initial height h at point P. The mass slides down the surface and around a frictionless loop of radlus R = 2 m. If the mormal force that the surface exerts on the mass when it is at the position Q is given by FN = 180 N, what is the height h? (A) 4.1 m (B) 7.2 m (C) 2.5 m (D) 3.8 m (E) 5.7 m
A small block slides down a frictionless ramp and around a vertical loop of radius 1.00-m, centered as shown at a height of 2.00-m above the base. Determine the minimum height, H, from which the block can be released on the ramp and still make it around the circular loop. Ignore the thickness of the block. {Hint. Find minimum KE at B using ∑Fn = mg and then use EA = EB}
A particle with mass m slips down on track ABC in the figure. Segment AB of the track is rough, while segment BC is smooth. The initial velocity of the particle in point A is zero. Data: R = 10 [m]; α = 60∘; m = 2 [kg]; μBc = 0,1; Δh2 = 6 [m]; g = 9,81 [m/s2]. a, Calculate the magnitude of the velocity of the particle in point B. b, Calculate the magnitude of the velocity of the particle in point C. c, Calculate the elapsed time between the B and C positions of the particle.
A proton is flying through space with an initial velocity v0 = 3.6×106 m/s, as shown below. It interacts with a fixed negative charge q = −13 nC along the path shown. What is its speed in m/s when it reaches the point P. given that x = 2.8 cm and y = 5.7 cm? Give your answer to 3 significant digits. (note the drawing may not be to scale)
A bead slides on a semicircular frictionless wire starting at a height of 0.5 m where it is at rest. The lowest point on the wire is 0.1 m high. Find the speed (in m/s) after the bead has passed through this minimum and has a height of 0.27 m. *Please submit your solution to the Learn dropbox (include QID) 1.5 m/s 2.12 m/s 3 m/s 3.88 m/s
The car has a constant speed vM and passes x = 0 at t = 0. The police motor starts at x = 0 with constant acceleration ap at t = t1 (with t1 > 0 ). (a) Calculate the time t at which the motorist and the police are at the same position. (b) When the police wants to catch the car at position x = XC, what acceleration ap should he/she have? Express ap in Xc, vM and t1.
Only two forces act on an object (mass = 2.72 kg), as in the drawing. Find the (a) magnitude and (b) direction (relative to the x axis) of the acceleration of the object.
A circular coil, formed by 200 turns of 10 cm radius, is located perpendicular to a magnetic field of 0.2 T. Determine the e.m.f. induced in the coil in the following cases referring to a time interval equal to 0.1 s: the magnetic field doubles; the magnetic field is canceled; the direction of the magnetic field is reversed; the coil is rotated 90∘ around the axis parallel to the magnetic field; the coil is rotated 90∘ around the axis perpendicular to the magnetic field.
Q1) A ball is thrown off a tower at 45 m/s at an angle of 60.0∘ above the horizontal. a) How long is the ball in the air? b) How far from the building did the ball land? c) What is the ball's velocity (magnitude and direction) just before it touches the ground? d) Find the maximum height the rock travel?
In the figure four particles form a square with edge length a = 2.21×10−2 m. The charges are q1 = q4 = 1.60×10−15 C and q2 = q3 = q. (a) What is q if the net electrostatic force on particle 1 is zero? (b) Is there any value of q that makes the net electrostatic force on each of the four particles zero? a) Number Units b)
In the figure particle 1 of charge q1 = 1.03 μC and particle 2 of charge q2 = −3.06 μC, are held at separation L = 9.2 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b)y coordinates of particle 3? (a) Number Units (b) Number Units
In the figure particle 1 of charge +4 e is above a floor by distance d1 = 4.20 mm and particle 2 of charge +7e is on the floor, at distance d2 = 7.10 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1? Number Units
Figure (a) shows a circular disk that is uniformly charged. The central z axis is perpendicular to the disk face, with the origin at the disk. Figure (b) gives the magnitude of the electric field along that axis in terms of the maximum magnitude Em at the disk surface. The z axis scale is set by zs = 9.0 cm. What is the radius of the disk? (a) (b) Number Units
A small, non-conducting ball of mass m and charge q (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ with a vertical uniformly charged plate with charge density σ. Considering the gravitational force on the charge, calculate the angle θ in terms of m, σ, q, and fundamental constants.
In a game of pool, ball A is moving with a velocity v0 of magnitude v0 = 15 ft/s when it strikes balls B and C, which are at rest and aligned as shown. Knowing that after the collision the three balls move in the directions indicated and assuming frictionless surfaces and perfectly elastic impact (that is, conservation of energy), determine the magnitudes of the velocities vA, vB, and vC.
A cook holds a 1.92-kg carton of milk at arm's length (see the figure below). What force F→B must be exerted by the biceps muscle? (Ignore the weight of the forearm. Give the magnitude.) N
A child in a boat throws a 5.85−kg package out horizontally with a speed of 10.0 m/s. Part A Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 27.0 kg and that of the boat is 40.0 kg. (Take the package's direction of motion as positive.)
In reaching her destination, a backpacker walks with an average velocity of 1.22 m/s, due west. This average velocity results, because she hikes for 5.91 km with an average velocity of 2.33 m/s due west, turns around, and hikes with an average velocity of 0.576 m/s due east. How far east did she walk (in kilometers)?
Chapter 02, Problem 10 In reaching her destination, a backpacker walks with an average velocity of 1.29 m/s, due west. This average velocity results, because she hikes for 6.02 km with an average velocity of 2.82 m/s due west, turns around, and hikes with an average velocity of 0.398 m/s due east. How far east did she walk (in kilometers)? Number Units
The girl throws 0.8 kg ball toward the wall with an initial velocity VA = 15 m/s as shown in Fig. 2. Parameters are given in Fig. 2. Ball is considered as a particle and there is not friction between the ball and the wall. Determine the velocity of the ball at which it strikes the wall at B. (10 marks) Calculate the velocity of the ball at which it rebounds from the wall if the coefficient of restitution e = 0.6. (15 marks) Determine the distance s (see Fig. 2) from the wall to where it strikes the ground at C. (15 marks)
The figure below shows an end view of a single-turn square loop of metal wire in the center of and coaxial with a very long solenoid with a circular cross section. The solenoid is 21.0 cm long, has a radius r = 3.00 cm, and consists of 126 turns of wire. The length of each side of the square loop is ℓ = 1.50 cm. (a) The current in the solenoid is 4.00 A. What is the magnetic flux through the square loop (in T⋅m2)? T⋅m2 (b) The current decreases from 4.00 A to zero in 4.00 s. What is the magnitude of the average induced emf in the square loop (in V ) over this time? V
An ac generator provides emf to a resistive load in a remote factory over a two-cable transmission line. At the factory a step-down transformer reduces the voltage from its (rms) transmission value Vt to a much lower value that is safe and convenient for use in the factory. The transmission line resistance is 0.35 Ω /cable, and the power of the generator is 277 kW. If Vt = 92 kV, what are (a) the voltage decrease ΔV along the transmission line and (b) the rate Pd at which energy is dissipated in the line as thermal energy? If Vt = 9.6 kV, what are (c) ΔV and (d) Pd? If Vt = 0.84 kV, what are (e) ΔV and (f) Pd?
A wire with current i = 1.79 A is shown in the figure. Two semi-infinite straight sections, both tangent to the same circle with radius 7.04 cm, are connected by a circular arc that has a central angle θ and runs along the circumference of the circle. The connecting arc and the two straight sections all lie in the same plane. If B = 0 at the center of the circle, what is θ? Number Units
At a football tryout, a player runs a 40-yard dash in t2 = 4.60 seconds. If the reaches his maximum speed at the 13-yard mark L1 with a constant acceleration and then maintains that speed for the remainder of the run, determine his acceleration over the first 13 yards, his maximum speed, and the time duration of the acceleration. Answers: His acceleration: a = ft/sec2 His maximum speed: V = ft/sec The time duration of the acceleration: t = sec
One particle has a mass of 3.64×10−3 kg and a charge of +6.55 μC. A second particle has a mass of 7.71×10−3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.173 m, the speed of the 3.64 x 10−3 kg-particle is 165 m/s. Find the initial separation between the particles.
A golfer hits a ball with an initial velocity of magnitude v0 at an angle a with the horizontal. The ball must clear the tops of two trees and land as close as possible to the flag. Determine v0 and the distance d when the golfer uses a five-iron with a = 26.5∘. When the golfer uses a five-iron with a = 26.5∘, v0 is calculated to be m/s. When the golfer uses a five-iron with a = 26.5∘, the distance is m. Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
The accompanying figure shows a long, straight wire carrying a current of 10 A. What is the magnetic force (in N) on an electron at the instant it is 26 cm from the wire, traveling parallel to the wire with a speed of 3.0×105 m/s? (Enter the magnitude.) 10 A N Describe qualitatively the subsequent motion of the electron. The electron continues to move parallel to the wire. The electron moves toward the wire. The electron moves away from the wire.
Two particles each have a mass of 6.4×10−4 kg. One has a charge of +6.1×10−6 C, and the other has a charge of −6.1×10−6 C. They are initially held at rest at a distance of 1.1 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-third its initial value? Number Units
Chapter 18, Problem 47 A particle of charge +16.0 μC and mass 3.54×10−5 kg is released from rest in a region where there is a constant electric field of +686 N/C. What is the displacement of the particle after a time of 1.35×10−2 s? Number Units
A golfer hits a golf ball from Point A with an initial velocity of 53 m/s at an angle of 25∘ with the horizontal. Determine the radius of curvature of the trajectory described by the ball at the highest point of the trajectory. The radius of curvature of the trajectory described by the ball at the highest point of the trajectory is m. Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
A golf ball is struck with a velocity of vA = 70 ft/s as shown. Part A Determine the speed at which the ball strikes the ground at B. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part. ANSWER: vB = Part B Determine the time of flight from A to B. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part. ANSWER: t =
A sphere uniformly distributed with matter has radius a and total mass 2M. This sphere is surrounded by a thick shell of inner radius b and outer radius c, and total mass 4M. Knowns: G, a b, c a) What is the gravitational field for r < a ? b) What is the gravitational field for a < r < b? c) What is the gravitational field for b < r < c? d) What is the gravitational field for r > c? Φ = ∮g→⋅dA→ = 4πGMEnclosed
One particle has a mass of 4.50×10−3 kg and a charge of +8.90 μC. A second particle has a mass of 8.35×10−3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.138 m, the speed of the 4.50×10−3 kg-particle is 138 m/s. Find the initial separation between the particles. Number Units
A positive charge +q1 is located to the left of a negative charge −q2. On a line passing though the two charges, there are two places where the total potential is zero. The first place is between the charges and is 3.09 cm to the left of the negative charge. The second place is 8.17 cm to the right of the negative charge. (a) What is the distance between the charges? (b) Find q1/q2, the ratio of the magnitudes of the charges. (a) Number Units (b) Number Units Review Conceptual Example 7 as background for this problem.
A conducting wire of radius r and length L has resistance of R = 19 Ω. Find the resistance of another wire that is made of the same material but has twice of the length and half of the radius.
a. A conducting bar is bent into a U-shape as shown below, with a sliding conductor placed across it. The sliding conductor moves at a constant velocity v→ = 100 ms in the presence of a time-varying magnetic field, B→ = a^z0.05 sin(1000πt) T. If d = 0.5 m, determine the total emf developed in the loop at t = 3.25 ms. In what direction would current be at this time? Answer: Vemf = +19.8 V, current is CCW b. A square loop of wire is 25 cm on each side and has a resistance of 125 Ω/m. The loop lies in the z = 0 plane with its corners at (0, 0, 0), (0.25, 0, 0), (0.25, 0.25, 0), and (0, 0.25, 0) at t = 0. The loop is moving with velocity vy = 50 m/s in a B-field given by B→ = a^z8 cos(1.5×108t − 0.5x) μT. Determine a function of time which expresses the ohmic power being delivered to the loop and then evaluate the expression at t = 5.00145281 ms. Answer: 20.9 W
A circular loop of wire rests on a table. A long, straight wire lies on this loop, directly over its center, as the drawing illustrates. The current I in the straight wire is decreasing. In what direction (clockwise, counterclockwise or no direction since there is no induced current) is the induced current, if any, in the loop?
A mass (M1 = 5.0 kg) is connected by a light cord to a mass (M2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s2. What is the moment of inertia of the pulley?
You have a block (m = 5.2 kg) on a ramp like so (θ = 25∘) : What is the minimum coefficient of static friction that will keep this block from moving?
A constant current I0 is present in a conducting loop as shown in the figure. a) Find the vector potential A and the magnetic field B at the center, P(0, 0, 0). b) Find the vector potential, A, at any point on z-axis. Is it possible to get B from this calculated A?
Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression B = 3.00t3 − 2.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.40 cm. (a) When t = 2.00 s, calculate the magnitude of the force exerted on an electron located at point P1, which is at a distance r1 = 4.80 cm from the center of the circular field region. N (b) When t = 2.00 s, calculate the direction of the force exerted on an electron located at point P1, which is at a distance r1 = 4.80 cm from the center of the circular field region. tangent to the electric field line passing through point P1 and clockwise tangent to the electric field line passing through point P1 and counterclockwise The magnitude is zero. (c) At what instant is this force equal to zero? (Consider the time after t = 0 s.) s
(a)Two charges are placed on the x-axis: one is placed at x = 3 m and the other is at x = −3 m. The magnitude of both charges is 8.1 μC but the blue one (at x = −3 m ) is positive while the red one ( at x = +3 m) is negative. What are the x - and y-components of the electric field at (x, y) = (0 m, +4 m) ? Ex = N/C Ey = N/C (b) Now the positive and negative charge switch places. The magnitude of the charges is still 8.1 μC where the blue one (now at x = +3 m ) is positive and the red one (now at x = −3 m) is negative. What are the x - and y-components of the electric field at (x, y) = (0 m, +4 m) ? Ex = N/C Ey = N/C
Two horizontal forces, F1→ and F→2, are acting on a box, but only F→1 is shown in the drawing. F2→ can point either to the right or to the left. The box moves only along the x axis. There is no friction between the box and the surface. Suppose that F→1 = +5.4 N and the mass of the box is 4.4 kg. Find the magnitude and direction of F→2 when the acceleration of the box is (a) +5.7 m/s2, (b) −5.7 m/s2, and (c) 0 m/s2. (a) F2→ = (b) F→2 = (c) F→2 =
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 3.5 s. If R = 1.0 m and m = 3.9 kg, calculate the angular momentum about that axis.
At the instant of the figure, a 6.50 kg particle P has a position vector r→ of magnitude 1.30 m and angle θ1 = 45.0∘ and a velocity vector v→ of magnitude 6.90 m/s and angle θ2 = 31.0∘. Force F→, of magnitude 3.60 N and angle θ3 = 31.0∘ acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle?
A 0.64-kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstretched length triples. What is the mass of the second block?
Center of Mass (a) You are given the velocities of five particles as shown below in Fig. 3. Figure 3 Calculate the velocity of the center of mass (CM) of the system of particles. (b) Find the centre of mass of a uniform plate (shown in Fig. 4) having semicircular inner and outer boundaries of radii R1, and R2.
A yo-yo (mass m, radius r ) is rolling down on a massless wire, which is fixed to the ceiling. Given: m = 0.10 kg, r = 0.04 m, IG = 1.2×10−4 kgm2, g = 9.81 m/s2 Determine the acceleration aG (in m/s2 ) of the center of gravity. MAD FBD Hint: When formulating a kinematic relationship think about the location of the ICoR.
Blocks A and B are of identical size and mass, m. The long side of each block is 2a while the short side is a. The force P acts on block A at mid-height (see picture). The coefficient of friction between block A and B is μs,AB and the coefficient of friction between block B and surface C is μs,BC = 0. Assume that static and kinematic friction are equal, i.e., μs,BC = μk,BC and μs,AB = μk,AB. What is the maximum P that can be applied so that block A does not tip?
Consider the 3 figures below A, B and C. (a) In Fig. (A). The current I through a wire is up, and the force F→ is left. What direction is the magnetic field B→ ? (b) Fig. (B). What is the direction of the velocity v→ of a positive charge here? (c) Fig. (C). A negative charge travels right, and B→ is into page. What direction is the Force F→ ? (a) (b) (c)
What will the acceleration of the 3 kg block on the table be when a 20 N constant downward force is applied to the cable on the left and a 2.6 kg mass hangs on the right? Include both magnitude and direction of the resulting acceleration.
A mass on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its equation of motion is x(t) = 4 sin(t), where t is measured in seconds and x in centimeters. (a) Find the velocity and acceleration at time t. v(t) = a(t) = (b) Find the position, velocity, and acceleration of the mass at time t = 2π/3. x(2π 3) = v(2π 3) = a(2π 3) = In what direction is the mass moving at that time? Since v(2π 3) 0, the mass is moving to the
Satellite A moving in the circular orbit and satellite B moving in the elliptical orbit collide and become entangled at point C. If the masses of the satellites are equal, determine the maximum altitude hmax of the resulting orbit. Assume hC = 854 mi, Δh = 224 mi. Answer: hmax = mi
The 200-kg glider B is being towed by airplane A, which is flying horizontally with a constant speed of v = 208 km/h. The tow cable has a length r = 64 m and may be assumed to form a straight line. The glider is gaining altitude and when θ reaches 15∘, the angle is increasing at the constant rate θ = 7 deg/s. At the same time the tension in the tow cable is 2220 N for this position. Calculate the aerodynamic lift L and drag D acting on the glider. Assume ϕ = 13∘
The tank in the form of a right-circular cone of radius 11 feet and height 38 feet standing on its end, vertex down, is leaking through a circular hole of radius 4 inches. Assume the friction coefficient to be c = 0.6 and g = 32 ft/s2. Then the equation governing the height h of the leaking water is dh dt = If the tank is initially full, it will take it seconds to empty.
A device called a railgun uses the magnetic force on currents to launch projectiles at very high speeds. An idealized model of a railgun is illustrated in the following figure. A 1.2 volt power supply is connected to the two conducting rails. A segment of copper wire, in a region of uniform magnetic field, freely slides on the rails. The wire has a 0.85 mΩ resistance and a mass of 5.0 g. Ignoring the resistance of the rails, when the power supply is connected a) what is the current in the circuit? b) what are the magnitude and direction of the force on the wire? c) what will be the wire's speed after it has slid a distance of 1.0 mm?
Two flat conducting plates are arranged parallel to each other with one on the left and one on the right. The plates are circular with a radius R and are separated by a distance L with L being much smaller than R(L << R). The charge on the left plate is negative (−Q) and the plate on the right is positive (+Q). What is the electric field in the gap between the plates? 2Q 4ϵoπL2 pointing to the right. Q ϵoπR2 pointing to the right. Q ϵoπR2 pointing to the left. 2Q 4ϵoπL2 pointing to the left.
In the figure, the particles have charges q1 = −q2 = 738 nC and q3 = −q4 = 98.2 nC, and distance a = 6.06 cm. What are the (a) x and (b) y components of the net electrostatic force on particle 3? (a) Number Units (b) Number Units
In the figure particle 1 of charge +5e is above a floor by distance d1 = 5.20 mm and particle 2 of charge +7e is on the floor, at distance d2 = 7.20 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1? Number Units
At a certain location, the horizontal component of the earth's magnetic field is 2.1×10−5 T, due north. A proton moves eastward with just the right speed, so the magnetic force on it balances its weight. Find the speed of the proton. Number Units
Building an Adjustable Electromagnet. You and your team are tasked with designing a source to provide a uniform magnetic field for an experiment. The field inside a solenoid is uniform, provided that the length of the solenoid is much longer than its diameter. One useful characteristic of an electromagnet of this type is that the field inside can be adjusted anywhere between 0 T and some maximum value by controlling the current. In addition, the direction of the field, which is always pointed along the axis, can be reversed by reversing the current. The solenoid you are designing must be 3.60 cm in diameter and 25.0 cm long, and must generate a maximum magnetic field of magnitude B = 0.150 T. You intend to wind a cylinder of the given dimensions with wire that can safely pass a maximum current of 6.50 A. (a) How many windings should the solenoid have in order that the magnetic field at the center of the solenoid is 0.150 T when the current is 6.50 A? (b) What total length of wire is required? (c) What current should you pass through the coil to generate a smaller magnetic field of magnitude 3.50×10−2 T at its center, but directed antiparallel to the field generated in part (a)? Assume the current was positive in part (a). (a) Number Units (b) Number Units (c) Number Units
The x, y, and z components of a magnetic field are Bx = 0.15 T, By = 0.16 T, and Bz = 0.15 T. A 36−cm wire is oriented along the z axis and carries a current of 6.1 A. What is the magnitude of the magnetic force that acts on this wire? Number Units
In a certain region, the earth's magnetic field has a magnitude of 4.5×10−5 T and is directed north at an angle of 60∘ below the horizontal. An electrically charged bullet is fired north and 15∘ above the horizontal, with a speed of 720 m/s. The magnetic force on the bullet is 3.9×10−10 N, directed due east. Determine the bullet's electric charge, including its algebraic sign (+ or -). Number Units
The drawing shows a wire composed of three segments, AB, BC, and CD. There is a current of I = 2.4 A in the wire. There is also a magnetic field B (magnitude = 0.19 T) that is the same everywhere and points in the direction of +z axis. The lengths of the wire segments are LAB = 1.4 m, LBC = 0.3 m, and LCD = 0.3 m. Find the magnitude of the force that acts on each segment. FAB = FBC = FCD =
A 3.30−μC charge is moving with a speed of 4.90×104 m/s parallel to a very long, straight wire. The wire is 7.20 cm from the charge and carries a current of 50.0 A. Find the magnitude of the force on the charge. Number Units Multiple-Concept Example 7 discusses how problems like this one can be solved.
In the figure four particles form a square with edge length a = 2.44×10−2 m. The charges are q1 = q4 = 1.77×10−15 C and q2 = q3 = q. (a) What is q if the net electrostatic force on particle 1 is zero? (b) Is there any value of q that makes the net electrostatic force on each of the four particles zero? a) Number Units b)
Two long, straight wires are oriented perpendicular to the xy-plane. They carry currents of equal magnitude Iin opposite directions as shown in the figure. What is the direction of the magnetic field due to these currents at point P?
Shown in the figure below is a magazine resting on top of a book. There is static friction between the magazine and the book and there is kinetic friction between the book and the table. If you pull very gently on the book, both objects slide together. If you pull very forcefully, you will slide the book out from under the magazine. In this problem, we will determine the MAXIMUM FORCE that you can apply and still have the magazine come along for the ride. The characteristics of the system are given here: m1 = 0.35 kg m2 = 1.01 kg μs = 0.33 μk = 0.22 Answer all the following: What is the normal force, N1, of the book on the magazine? N What is the normal force, N2, of the table on the book? N What is the acceleration, a of the system? m/s2 What is the force applied, Fmax? N
is no friction between block A and the tabletop. The mass of block B is 4.90 kg. The pulley rotates about a frictionless axle, and the light rope doesn't slip on the pulley surface. The pulley has radius 0.200 m and moment of inertia 1.30 kg⋅m2. Part A If the pulley is rotating with an angular speed of 8.00 rad/s after the block has descended 1.20 m, what is the mass of block A ? Express your answer with the appropriate units.
The 91-kg man with center of mass G supports the 31-kg drum as shown. Find the greatest distance x at which the man can position himself without slipping if the coefficient of static friction between his shoes and the ground is 0.30.
A heavy sled is being pulled by two people as shown in the figure. The coefficient of static friction between the sled and the ground is μs = 0.643, the coefficient of kinetic friction is μk = 0.405, and the combined mass of the sled and its load is m = 351 kg. The ropes are separated by an angle ϕ = 25∘, and they make an angle θ with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension Tmin required to get the sled moving? Tmin =
In the figure shown. Determine F and N on the ground surface while a force P starts block A up the inclined surface of B. the weight of A is 100 kN and the angle of friction for all surfaces of contact is 15∘.
A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. As the drawing shows, one person hits the water 5.00 m from the end of the slide in a time of 0.715 s after leaving the slide. Ignore friction and air resistance, find the height H in the drawing.
(c) A 30-tonne concrete mixer truck travelling down the 10∘ inclined road at a speed of 8 m/s, as shown in Figure Q1.1. The coefficient of kinetic friction between the wheels and the road is μk = 0.5. Figure Q1.1 (i) Draw the free-body diagram of all forces exerted on the truck, (ii) Determine how far x the tyres skid on the road if the driver jams on the brakes, causing his wheels to lock. Use the principle of work and energy in solving for x.
Problem 8 A brick with mass m = 2.0 kg is moved upwards a vertical wall under the influence of a force F→. The force has a magnitude of 40 N and the angle α between the force and the vertical is equal to 35∘ (see Fig. 4). The coefficient of dynamic friction between the brick and the wall is k = 0.25. Find the acceleration of the brick. Please include a free body diagram and a well defined coordinate system in your solution. Figure 4: Object moved up a wall
At the instant of the figure, a 9.60 kg particle P has a position vector r→ of magnitude 7.00 m and angle θ1 = 45.0∘ and a velocity vector v→ of magnitude 5.00 m/s and angle θ2 = 32.0∘. Force F→, of magnitude 8.40 N and angle θ3 = 32.0∘ acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? (a) Number Units (b) Number Units
A car with a mass of 980 kg is initially traveling east toward an intersection with a speed of vc = 19.6 m/s and a 1500 kg pickup is traveling north toward the same intersection. The car and truck collide at the intersection and stick together. After the collision, the wreckage (car and truck) moves off in a direction of 40.0∘ above the x-axis. Determine the initial speed of the truck in meters per second. 11 m/s 10.4 m/s 10.7 m/s 10.1 m/s
Two highways intersect as shown in the figure below. At the instant shown, a police car P is distance, dP = 800 m, from the intersection and moving at speed VP = 80 km/h. Motorist M is distance, dM = 600 m, from the intersection and moving at speed VM = 60 km/h. A) In unit-vector notation, what is the velocity of the motorist with respect to the police car? (2.5 pts.) B) What is your answer to part (A) in magnitude and orientation form? (2.5 pts.) C) For the instant shown in the figure, what is the angle between the velocity found in (A) and the line of sight between the two cars? (2.5 pts.) D) If the cars maintain their velocities, do the answers to (A) and (B) change as the cars move nearer the intersection? ( 2.5 pts.)
A car with a mass of 980 kg is initially traveling east toward an intersection with a speed of vc = 17.9 m/s and a 1500 kg pickup is traveling north toward the same intersection. The car and truck collide at the intersection and stick together. After the collision, the wreckage (car and truck) moves off in a direction of 43.0∘ above the x-axis. Determine the initial speed of the truck and the final speed of the wreckage in meters per second. initial speed of the truck final speed of the wreckage the wreckage
A car with a mass of 980 kg is initially traveling east toward an intersection with a speed of vc = 19.5 m/s and a 1500 kg pickup is traveling north toward the same intersection. The car and truck collide at the intersection and stick together. After the collision, the wreckage (car and truck) moves off in a direction of 39.0∘ above the x-axis. Determine the initial speed of the truck and the final speed of the wreckage in meters per second. initial speed of the truck m/s final speed of the wreckage m/s
A particle starts from rest and accelerates as shown in the figure below. (a) Determine the particle's speed at t = 10.0 s and at t = 20.0 s. t = 10.0 s m/s t = 20.0 s m/s (b) Determine the distance traveled in the first 20.0 s. (Enter your answer to one decimal place.) m
A concave mirror has a focal length of 34.0 cm. The distance between an object and its image is 49.6 cm. Find (a) the object and (b) image distances, assuming that the object lies beyond the center of curvature and (c) the object and (d) image distances, assuming that the object lies between the focal point and the mirror. (a) Number Units (b) Number Units (c) Number Units (d) Number Units Units
The order of most to least potential energy is letter B has the most, then C and then A. A car (represented by the blue dot) moves along the curved track. What is the direction of normal force FN on the driver when the car reaches the lowest point 'A' of the curve? Upward Backward Downward Forward
In the diagram below a 42, 336 kg car starts from rest at point A. It then slides down the hill, travels around the loop (the loop's diameter is 88 m). When the car is at point B, it is going the minimum possible speed it could be going without falling. After completing the loop, it compresses a spring 8.4 m. Assume there's no friction present. A.) Determine how high point A is above point C. B. ) Determine the spring constant.
On a frictionless horizontal surface, a 9.84 kg block is pushed up against a 98,400 N/m spring and compresses it 0.25 m. The block is then released. A.) Determine the block's speed after it leaves the spring. v = B.) The block then moves up a hill that is not frictionless. Determine what height the block reaches if 1752 J of thermal energy is produced. h =
The x, y, and z components of a magnetic field are Bx = 0.15 T, By = 0.16 T, and Bz = 0.15 T. A 36−cm wire is oriented along the z axis and carries a current of 6.1 A. What is the magnitude of the magnetic force that acts on this wire? Number Units
Air track collision. A target glider with mass m2 = 380 g is at rest on an air track at distance d = 73 cm from the track's end. A projectile glider with mass m1 = 660 g approaches the target glider with velocity v1i = −59 cm/s on an x axis along the track (figure a). It collides elastically with the target glider, and then the target glider hits and rebounds with the same speed from a short spring at its end of the track, the left end. That glider then catches up and collides elastically with the projectile glider for a second time (figure b). (a) How far from the left end of the track does this second collision occur? (b) If we halve the initial speed of glider 1 , what then is the answer? (a) (b)
Problem 5: Consider the projectile motion of the ball shown in the figure. The initial velocity of the ball is vo = 30 m/s and it is thrown at an angle θ = 40∘ above the horizontal. The ball just clears the fence 20 m from its initial position. Determine: Find the maximum height H, the time it takes the particle to reach point C, and the total horizontal range L that the particle travels. a. Maximum height H of the fence in meters 5 points b. The time it takes the particle to reach point C in seconds. 5 points c. The total horizontal range L that the particle travels from A to C in meters. 5 points
Problem 13.176 Direct central impact between a ball and a plate- Dependent multi-part problem assign all parts NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A 0.25−lb ball thrown with a horizontal velocity v0 strikes a 1.5−lb plate attached to a vertical wall at a height of 36 in. above the ground. It is observed that after rebounding, the ball hits the ground at a distance of 24 in. from the wall when the plate is rigidly attached to the wall (Figure 1) and at a distance of 10 in. when a foam-rubber mat is placed between the plate and the wall (Figure 2). Problem 13.176. a Direct central impact between a ball and a steel plate Determine the coefficient of restitution e between the ball and the plate. The coefficient of restitution e is
From the same height (and at the same time), one ball is dropped, and another ball is fired horizontally. Which one will hit the ground first? they both hit the ground at the same time it depends on the initial height the "dropped" ball the "fired" ball it depends on how hard the ball was fired In the previous problem, which ball has the greater velocity at ground level? neither-they both have the same velocity on impact the "fired" ball it depends on how hard the ball was thrown the "dropped" ball
A 6 kg ball is attached to the end of a long string. The ball revolves with a constant speed of 3 m/s in a 4 m radius horizontal circle that forms a conical pendulum. Calculate the work done on the ball by the tension force WT. [MAKE SURE TO INCLUDE UNIT IN YOUR ANSWER!!!]
A ball is thrown straight up from a rooftop 192 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown. h = −16t2 + 16t + 192 The ball hits the ground after seconds. Each tick represents second(s).
A 5.11 kg ball is attached to the top of a vertical pole with a 2.01 m length of massless string. The ball is struck, causing it to revolve around the pole at a speed of 4.07 m/s in a horizontal circle with the string remaining taut. Use g = 9.81 m/s2. Calculate the angle θ, between 0∘ and 90∘, that the string makes with the pole. θ = What is the tension T of the string? T = N
Figure Q1.2 illustrates a crate with the mass of mc, which is initially at rest at a slope with angle of θ. A bullet of mass mb and velocity ub is fired into the crate and causes it to slide along the slope embedding itself in the crate. The coefficient of friction between the surface of the slope and the crate is given by μ. Ignore the aerodynamic drag during the process. Note that mc, θ, mb, ub, and μ are generated randomly. Determine: The velocity, (denoted v1 ), of the crate after moving L1, which is defined randomly The total travelled distance L The total mechanical energy lost during the process Figure Q1.2