College Physics 7th Edition solutions

College Physics 7
A 0.40-kg object is attached to a spring with force constant 160 N/m so that the object is allowed to move on a horizontal frictionless surface. The object is released from rest when the spring is compressed 0.15 m. Find (a) the force on the object and (b) its acceleration at that instant.

College Physics 7
A load of 50 N attached to a spring hanging vertically stretches the spring 5.0 cm. The spring is now placed horizontally on a table and stretched 11 cm. (a) What force is required to stretch the spring by that amount? (b) Plot a graph of force (on the y-axis) versus spring displacement from the equi

College Physics 7
A ball dropped from a height of 4.00 m makes a perfectly elastic collision with the ground. Assuming that no mechanical energy is lost due to air resistance, (a) show that the motion is periodic and (b) determine the period of the motion. (c) Is the motion simple harmonic? Explain.

College Physics 7
A small ball is set in horizontal motion by rolling it with a speed of 3.00 m/s across a room 12.0 m long between two walls. Assume that the collisions made with each wall are perfectly elastic and that the motion is perpendicular to the two walls. (a) Show that the motion is periodic and determine

College Physics 7
A spring is hung from a ceiling, and an object attached to its lower end stretches the spring by a distance of 5.00 cm from its unstretched position when the system is in equilibrium. If the spring constant is 47.5 N/m, determine the mass of the object.

College Physics 7
An archer must exert a force of 375 N on the bowstring shown in Figure P13.6a (page 452) such that the string makes an angle of   35.0 with the vertical. (a) Determine the tension in the bowstring. (b) If the applied force is replaced by a stretched spring as in Figure P13.6b, and the spring is st

College Physics 7
A slingshot consists of a light leather cup containing a stone. The cup is pulled back against two parallel rubber bands. It takes a force of 15 N to stretch either one of these bands 1.0 cm. (a) What is the potential energy stored in the two bands together when a 50-g stone is placed in the cup and

College Physics 7
An archer pulls her bowstring back 0.400 m by exerting a force that increases uniformly from zero to 230 N. (a) What is the equivalent spring constant of the bow? (b) How much work is done in pulling the bow?

College Physics 7
A childs toy consists of a piece of plastic attached to a spring (Fig. P13.9). The spring is compressed against the oor a distance of 2.00 cm, and the toy is released. If the toy has a mass of 100 g and rises to a maximum height of 60.0 cm, estimate the force constant of the spring.

College Physics 7
An automobile having a mass of 1 000 kg is driven into a brick wall in a safety test. The bumper behaves like a spring with constant 5.00  106 N/m and is compressed 3.16 cm as the car is brought to rest. What was the speed of the car before impact, assuming that no energy is lost in the collision wi

College Physics 7
A simple harmonic oscillator has a total energy E. (a) Determine the kinetic and potential energies when the displacement is one-half the amplitude. (b) For what value of the displacement does the kinetic energy equal the potential energy?

College Physics 7
A 1.50-kg block at rest on a tabletop is attached to a horizontal spring having constant 19.6 N/m, as in Figure P13.12. The spring is initially unstretched. A constant 20.0-N horizontal force is applied to the object, causing the spring to stretch. (a) Determine the speed of the block after it has mo

College Physics 7
A 10.0-g bullet is red into, and embeds itself in, a 2.00-kg block attached to a spring with a force constant of 19.6 N/m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of 300 m/s just before it strikes the block and the block slides on a frictionless surface

College Physics 7
A 1.5-kg block is attached to a spring with a spring constant of 2 000 N/m. The spring is then stretched a distance of 0.30 cm and the block is released from rest. (a) Calculate the speed of the block as it passes through the equilibrium position if no friction is present. (b) Calculate the speed of

College Physics 7
A 0.40-kg object connected to a light spring with a force constant of 19.6 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest, determine (a) the maximum speed of the object, (b) the speed of the object when the spring is compressed 1.5 cm, a

College Physics 7
An objectspring system oscillates with an amplitude of 3.5 cm. If the spring constant is 250 N/m and the object has a mass of 0.50 kg, determine (a) the mechanical energy of the system, (b) the maximum speed of the object, and (c) the maximum acceleration of the object.

College Physics 7
At an outdoor market, a bunch of bananas is set into oscillatory motion with an amplitude of 20.0 cm on a spring with a force constant of 16.0 N/m. It is observed that the maximum speed of the bunch of bananas is 40.0 cm/s. What is the weight of the bananas in newtons?

College Physics 7
A 50.0-g object is attached to a horizontal spring with a force constant of 10.0 N/m and released from rest with an amplitude of 25.0 cm. What is the velocity of the object when it is halfway to the equilibrium position if the surface is frictionless?

College Physics 7
While riding behind a car traveling at 3.00 m/s, you notice that one of the cars tires has a small hemispherical bump on its rim, as in Figure P13.19. (a) Explain why the bump, from your viewpoint behind the car, executes simple harmonic motion. (b) If the radius of the cars tires is 0.30 m, what is

College Physics 7
An object moves uniformly around a circular path of radius 20.0 cm, making one complete revolution every 2.00 s. What are (a) the translational speed of the object, (b) the frequency of motion in hertz, and (c) the angular speed of the object?

College Physics 7
Consider the simplied single-piston engine in Figure P13.21. If the wheel rotates at a constant angular speed , explain why the piston rod oscillates in simple harmonic motion.

College Physics 7
The frequency of vibration of an objectspring system is 5.00 Hz when a 4.00-g mass is attached to the spring. What is the force constant of the spring?

College Physics 7
A spring stretches 3.9 cm when a 10-g object is hung from it. The object is replaced with a block of mass 25 g that oscillates in simple harmonic motion. Calculate the period of motion.

College Physics 7
When four people with a combined mass of 320 kg sit down in a car, they nd that the car drops 0.80 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the cars vibration if its mass (when it is empty) is 2.0  103 kg?

College Physics 7
A cart of mass 250 g is placed on a frictionless horizontal air track. A spring having a spring constant of 9.5 N/m is attached between the cart and the left end of the track. When in equilibrium, the cart is located 12 cm from the left end of the track. If the cart is displaced 4.5 cm from its equil

College Physics 7
The motion of an object is described by the equation Find (a) the position of the object at t  0 and t  0.60 s, (b) the amplitude of the motion, (c) the frequency of the motion, and (d) the period of the motion.

College Physics 7
A 2.00-kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 5.00N/m. The object is displaced 3.00m to the right from its equilibrium position and then released, initiating simple harmonic motion. (a) What is the force (magnitude and direct

College Physics 7
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is the

College Physics 7
Given that x  A cos ( t) is a sinusoidal function of time, show that v (velocity) and a (acceleration) are also sinusoidal functions of time. [Hint: Use Equations 13.6 and 13.2.]

College Physics 7
A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the oor and that its period is 15.5 s. (a) How tall is the tower? (b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s2, what is the period there?

College Physics 7
A simple 2.00-m-long pendulum oscillates at a location where g  9.80 m/s2. How many complete oscillations does it make in 5.00 min?

College Physics 7
An aluminum clock pendulum having a period of 1.00 s keeps perfect time at 20.0C. (a) When placed in a room at a temperature of 5.0C, will it gain time or lose time? (b) How much time will it gain or lose every hour? [Hint: See Chapter 10.]

College Physics 7
A pendulum clock that works perfectly on Earth is taken to the Moon. (a) Does it run fast or slow there? (b) If the clock is started at 12:00 midnight, what will it read after one Earth day (24.0 h)? Assume that the free-fall acceleration on the Moon is 1.63 m/s2.

College Physics 7
A simple pendulum is 5.00 m long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What is the period of simple harmonic motion for the

College Physics 7
The free-fall acceleration on Mars is 3.7 m/s2. (a) What length of pendulum has a period of 1 s on Earth? What length of pendulum would have a 1-s period on Mars? (b) An object is suspended from a spring with force constant 10 N/m. Find the mass suspended from this spring that would result in a perio

College Physics 7
A cork on the surface of a pond bobs up and down two times per second on ripples having a wavelength of 8.50 cm. If the cork is 10.0 m from shore, how long does it take a ripple passing the cork to reach the shore?

College Physics 7
A wave traveling in the positive x-direction has a frequency of 25.0 Hz, as in Figure P13.37. Find the (a) amplitude, (b) wavelength, (c) period, and (d) speed of the wave.

College Physics 7
A bat can detect small objects, such as an insect, whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a frequency of 60.0 kHz, and if the speed of sound in air is 340 m/s, what is the smallest insect a bat can detect?

College Physics 7
If the frequency of oscillation of the wave emitted by an FM radio station is 88.0 MHz, determine (a) the waves period of vibration and (b) its wavelength. (Radio waves travel at the speed of light, 3.00  108 m/s.)

College Physics 7
The distance between two successive maxima of a transverse wave is 1.20 m. Eight crests, or maxima, pass a given point along the direction of travel every 12.0 s. Calculate the wave speed.

College Physics 7
A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?

College Physics 7
Ocean waves are traveling to the east at 4.0 m/s with a distance of 20 m between crests. With what frequency do the waves hit the front of a boat (a) when the boat is at anchor and (b) when the boat is moving westward at 1.0 m/s?

College Physics 7
A phone cord is 4.00 m long and has a mass of 0.200 kg. A transverse wave pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in 0.800 s. What is the tension in the cord?

College Physics 7
A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.800 s to reach the opposite tower, 20.0 m away. If a 1-m length of the rope has a mass of 0.350 kg, nd the tension in the tig

College Physics 7
Transverse waves with a speed of 50.0 m/s are to be produced on a stretched string. A 5.00-m length of string with a total mass of 0.060 0 kg is used. (a) What is the required tension in the string? (b) Calculate the wave speed in the string if the tension is 8.00 N.

College Physics 7
An astronaut on the Moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large object suspended from it. Assume a wire of mass 4.00g is 1.60m long and has a 3.00-kg object suspended from it. A pulse requires 36.1ms to traverse the length of the wire. Calculate

College Physics 7
A simple pendulum consists of a ball of mass 5.00 kg hanging from a uniform string of mass 0.0600 kg and length L. If the period of oscillation of the pendulum is 2.00 s, determine the speed of a transverse wave in the string when the pendulum hangs vertically.

College Physics 7
A string is 50.0 cm long and has a mass of 3.00 g. A wave travels at 5.00 m/s along this string. A second string has the same length, but half the mass of the rst. If the two strings are under the same tension, what is the speed of a wave along the second string?

College Physics 7
Tension is maintained in a string as in Figure P13.49. The observed wave speed is 24 m/s when the suspended mass is 3.0 kg. (a) What is the mass per unit length of the string? (b) What is the wave speed when the suspended mass is 2.0 kg?

College Physics 7
The elastic limit of a piece of steel wire is 2.70  109 Pa. What is the maximum speed at which transverse wave pulses can propagate along the wire without exceeding its elastic limit? (The density of steel is 7.86  103 kg/m3.)

College Physics 7
Transverse waves travel at 20.0 m/s on a string that is under a tension of 6.00 N. What tension is required for a wave speed of 30.0 m/s in the string?

College Physics 7
A series of pulses of amplitude 0.15 m is sent down a string that is attached to a post at one end. The pulses are reected at the post and travel back along the string without loss of amplitude. What is the amplitude at a point on the string where two pulses are crossing (a) if the string is rigidly

College Physics 7
A wave of amplitude 0.30 m interferes with a second wave of amplitude 0.20 m traveling in the same direction. What are (a) the largest and (b) the smallest resultant amplitudes that can occur, and under what conditions will these maxima and minima arise?

College Physics 7
The position of a 0.30-kg object attached to a spring is described by x  (0.25 m) cos(0.4 t) Find (a) the amplitude of the motion, (b) the spring constant, (c) the position of the object at t  0.30 s, and (d) the objects speed at t  0.30 s.

College Physics 7
A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f  1.50 Hz. Block B rests on it, as shown in Figure P13.55, and the coefcient of static friction between the two is  s  0.600. What maximum amplitude of oscillation can the system

College Physics 7
A 500-g block is released from rest and slides down a frictionless track that begins 2.00 m above the horizontal, as shown in Figure P13.56. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring with a spring constant of 20.0 N/m. Find the maximum

College Physics 7
A 3.00-kg object is fastened to a light spring, with the intervening cord passing over a pulley (Fig. P13.57). The pulley is frictionless, and its inertia may be neglected. The object is released from rest when the spring is unstretched. If the object drops 10.0 cm before stopping, nd (a) the spring

College Physics 7
A 5.00-g bullet moving with an initial speed of 400 m/s is red into and passes through a 1.00-kg block, as in Figure P13.58. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 900 N/m. If the block moves 5.00 cm to the right after imp

College Physics 7
A 25-kg block is connected to a 30-kg block by a light string that passes over a frictionless pulley. The 30-kg block is connected to a light spring of force constant 200 N/m, as in Figure P13.59. The spring is unstretched when the system is as shown in the gure, and the incline is smooth. The 25-kg

College Physics 7
A spring in a toy gun has a spring constant of 9.80 N/m and can be compressed 20.0 cm beyond the equilibrium position. A 1.00-g pellet resting against the spring is propelled forward when the spring is released. (a) Find the muzzle speed of the pellet. (b) If the pellet is red horizontally from a hei

College Physics 7
A 2.00-kg block hangs without vibrating at the end of a spring (k  500 N/m) that is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of g/3 when the acceleration suddenly ceases (at t  0). (a) What is the angular frequency of oscillation of the block after t

College Physics 7
An object of mass m is connected to two rubber bands of length L, each under tension F, as in Figure P13.62. The object is displaced vertically by a small distance y. Assuming the tension does not change, show that (a) the restoring force is (2F/L)y and (b) the system exhibits simple harmonic motion

College Physics 7
A light balloon lled with helium of density 0.180 kg/m3 is tied to a light string of length L  3.00 m. The string is tied to the ground, forming an inverted simple pendulum (Fig. P13.63a). If the balloon is displaced slightly from equilibrium, as in Figure P13.63b, show that the motion is simple har

College Physics 7
A light string of mass 10.0 g and length L  3.00 m has its ends tied to two walls that are separated by the distance D  2.00 m. Two objects, each of mass M  2.00 kg, are suspended from the string as in Figure P13.64. If a wave pulse is sent from point A, how long does it take to travel to point B?

College Physics 7
Assume that a hole is drilled through the center of the Earth. It can be shown that an object of mass m at a distance r from the center of the Earth is pulled toward the center only by the material in the shaded portion of Figure P13.65.Assume Earth has a uniform density  . Write down Newtons law of

College Physics 7
A 60.0-kg reghter slides down a pole while a constant frictional force of 300N retards his motion. A horizontal 20.0-kg platform is supported by a spring at the bottom of the pole to cushion the fall. The reghter starts from rest 5.00m above the platform, and the spring constant is 2500 N/m. Find (a)

College Physics 7
An object of mass m1  9.0 kg is in equilibrium while connected to a light spring of constant k  100 N/m that is fastened to a wall, as in Figure P13.67a. A second object, of mass m2  7.0 kg, is slowly pushed up against m1, compressing the spring by the amount A  0.20 m, as shown in Figure P13.67b

College Physics 7
An 8.00-kg block travels on a rough horizontal surface and collides with a spring. The speed of the block just before the collision is 4.00 m/s. As it rebounds to the left with the spring uncompressed, the block travels at 3.00 m/s. If the coefcient of kinetic friction between the block and the surfa

College Physics 7
Two points, A and B, on Earth are at the same longitude and 60.0 apart in latitude. An earthquake at point A sends two waves toward B. A transverse wave travels along the surface of Earth at 4.50 km/s, and a longitudinal wave travels through Earth at 7.80 km/s. (a) Which wave arrives at B rst? (b) W

College Physics 7
Figure P13.70 shows a crude model of an insect wing. The mass m represents the entire mass of the wing, which pivots about the fulcrum F. The spring represents the surrounding connective tissue. Motion of the wing corresponds to vibration of the spring. Suppose the mass of the wing is 0.30 g and the

College Physics 7
A 1.6-kg block on a horizontal surface is attached to a spring with a force constant of 1.0  103 N/m, as in Active Figure 13.1. The spring is compressed a distance of 2.0 cm, and the block is released from rest. (a) Calculate the speed of the block as it passes through the equilibrium position, x 

College Physics 7
Construct a simple pendulum by tying a metal bolt to one end of a string and taping the other end to the top of a doorframe. Adjust the length of the pendulum to be about 1.0 m, and measure it precisely. Obtain the period by timing 25 complete oscillations, making sure the string always makes small

College Physics 7
Attach one end of a rope (or a spring such as a Slinky) to a wall, stretch it taut, and use the system to study the following aspects of wave motion: (a) Send a pulse down the rope by striking it sharply from the side. An observer watching from the side can measure the time elapsed during 35 trips of