Show that the kinetic energy of a particle of mass m is related to the magnitude of the momentum p of that particle by KE = p2/2m. (Note: This expression is invalid for particles traveling at speeds near that of light.)
> Two masses m1 and m2, with m1 < m2, have equal kinetic energy. How do the magnitudes of their momenta compare? (a) Not enough information is given. (b) p1 < p2 (c) p1 = p2 (d) p1 > p2.
> While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 60. - kg person develops a power of 70. W during a race, how fast is the person running? (Assume a running step is 1.5 m long.)
> What average mechanical power must a 70.0 - kg mountain climber generate to climb to the summit of a hill of height 325 m in 45.0 min? Note: Due to inefficiencies in converting chemical energy to mechanical energy, the amount calculated here is only a fr
> A skier of mass 70.0 kg is pulled up a slope by a motordriven cable. (a) How much work is required to pull him 60.0 m up a 30.0° slope (assumed frictionless) at a constant speed of 2.00 m/s? (b) What power (expressed in hp) must a motor have to perform t
> An 80.0 - kg skydiver jumps out of a balloon at an altitude of 1.00 x 103 m and opens the parachute at an altitude of 200.0 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N with the parachute closed and constant at 3.60 x
> In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 4.0 m/s up a 20.0° inclined track. The combined mass of monkey and sled is 20. kg, and the coefficient of kinetic friction between sled and incline is 0.20. Ho
> A skier starts from rest at the top of a hill that is inclined 10.5° with respect to the horizontal. The hillside is 2.00 x 102 m long, and the coefficient of friction between snow and skis is 0.075 0. At the bottom of the hill, the snow is level and the
> A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravitational potential energy a
> A 2.1 x 103 - kg car starts from rest at the top of a 5.0 - m - long driveway that is inclined at 20.0° with the horizontal. If an average friction force of 4.0 x 103 N impedes the motion, find the speed of the car at the bottom of the driveway.
> A 25.0 - kg child on a 2.00 - m - long swing is released from rest when the ropes of the swing make an angle of 30.0° with the vertical. (a) Neglecting friction, find the child’s speed at the lowest position. (b) If the actual speed of the child at the l
> The system shown in Figure P5.43 is used to lift an object of mass m = 76.0 kg. A constant downward force of magnitude F is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rop
> A bowling ball onboard a space station is floating at rest relative to the station and an astronaut nudges a Ping-Pong ball toward it at speed υ, initiating a perfectly elastic head-on collision. Which answer is closest to the Ping-Pong ball’s speed afte
> An airplane of mass 1.50 x 104 kg is moving at 60.0 m/s. The pilot then increases the engine’s thrust to 7.50 x 104 N. The resistive force exerted by air on the airplane has a magnitude of 4.00 x 104 N. (a) Is the work done by the engine on the airplane
> (a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water flowing down it. Can the equation for conservation of mechanical energy be used on the child? (b) Is the ma
> (a) A block with a mass m is pulled along a horizontal surface for a distance x by a constant force F( at an angle θ with respect to the horizontal. The coefficient of kinetic friction between block and table is µk. Is the force exerted by friction equal
> The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5.39a. If the spring is compressed a distance of 0.120 m and the gun fired vertically as shown, the gun can launch a 20.0 - g projectile from rest t
> Two blocks are connected by a light string that passes over a frictionless pulley as in Figure P5.38. The system is released from rest while m2 is on the floor and m1 is a distance h above the floor. (a) Assuming m1 > m2, find an expression for the sp
> Tarzan swings on a 30.0 - m - long vine initially inclined at an angle of 37.0° with the vertical. What is his speed at the bottom of the swing a) If he starts from rest? (b) If he pushes off with a speed of 4.00 m/s?
> A block of mass m = 5.00 kg is released from rest from point Ⓐ and slides on the frictionless track shown in Figure P5.36. Determine (a) The block’s speed at points Ⓑ and Ⓒ and (b
> A 0.250 - kg block along a horizontal track has a speed of 1.50 m/s immediately before colliding with a light spring of force constant 4.60 N/m located at the end of the track. (a) What is the spring’s maximum compression if the track is frictionless? (b
> A 35.0 - cm long spring is hung vertically from a ceiling and stretches to 41.5 cm when a 7.50 - kg weight is hung from its free end. (a) Find the spring constant. (b) Find the length of the spring if the 7.50 - kg weight is replaced with a 195 - N weigh
> A child and a sled with a combined mass of 50.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 3.00 m/s at the bottom, what is the height of the hill?
> In a perfectly inelastic one-dimensional collision between two objects, what initial condition alone is necessary so that all of the original kinetic energy of the system is gone after the collision? (a) The objects must have momenta with the same magnit
> A 50. - kg pole vaulter running at 10. m/s vaults over the bar. Her speed when she is above the bar is 1.0 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.
> A horizontal spring attached to a wall has a force constant of 850 N/m. A block of mass 1.00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in Figure 5.22. The initial goal of this problem is to find the veloc
> A projectile of mass m is fired horizontally with an initial speed of υ0 from a height of h above a flat, desert surface. Neglecting air friction, at the instant before the projectile hits the ground, find the following in terms of m, υ0, h, and g: (a) T
> A 50.0 - kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 1.20 x 102 m/s from the top of a cliff 142 m above level ground, where the ground is taken to be y = 0. (a) What is the initial total mechanical energy of
> A flea is able to jump about 0.5 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100 - story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with
> The chin - up is one exercise that can be used to strengthen the biceps muscle. This muscle can exert a force of approximately 8.00 x 102 N as it contracts a distance of 7.5 cm in a 75 - kg male.3 (a) How much work can the biceps muscles (one in each arm
> Truck suspensions often have “helper springs” that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in Figure P5.26. When the main leaf spring is compr
> A daredevil on a motorcycle leaves the end of a ramp with a speed of 35.0 m/s as in Figure P5.25. If his speed is 33.0 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance. Figure P5.25
> Two blocks are connected by a light string that passes over two frictionless pulleys as in Figure P5.24. The block of mass m2 is attached to a spring of force constant k and m1 > m2. If the system is released from rest, and the spring is initially not
> A 2.10 x 103 - kg pile driver is used to drive a steel I - beam into the ground. The pile driver falls 5.00 m before coming into contact with the top of the beam, and it drives the beam 12.0 cm farther into the ground as it comes to rest. Using energy co
> A skater is using very low-friction rollerblades. A friend throws a Frisbee to her, on the straight line along which she is coasting. Describe each of the following events as an elastic, an inelastic, or a perfectly inelastic collision between the skater
> A 60.0 - kg athlete leaps straight up into the air from a trampoline with an initial speed of 9.0 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how d
> A block of mass 3.00 kg is placed against a horizontal spring of constant k = 875 N/m and pushed so the spring compresses by 0.070 0 m. (a) What is the elastic potential energy of the block–spring system? (b) If the block is now released and the surface
> A car accelerates uniformly from rest. Ignoring air friction, when does the car require the greatest power? (a) When the car first accelerates from rest, (b) Just as the car reaches its maximum speed, (c) When the car reaches half its maximum speed. (d)
> A 0.20 - kg stone is held 1.3 m above the top edge of a water well and then dropped into it. The well has a depth of 5.0 m. Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone–Earth system (a) Before the ston
> A certain truck has twice the mass of a car. Both are moving at the same speed. If the kinetic energy of the truck is K, what is the kinetic energy of the car? (a) K/4 (b) K/2 (c) 0.71K (d) K (e) 2K
> A large cruise ship of mass 6.50 x 107 kg has a speed of 12.0 m/s at some instant. (a) What is the ship’s kinetic energy at this time? (b) How much work is required to stop it? (c) What is the magnitude of the constant force required to stop it as it und
> Mark and David are loading identical cement blocks onto David’s pickup truck. Mark lifts his block straight up from the ground to the truck, whereas David slides his block up a ramp on massless, frictionless rollers. Which statement is true? (a) Mark doe
> A 7.80 - g bullet moving at 575 m/s penetrates a tree trunk to a depth of 5.50 cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet. (b) Assuming the frictional force is constant, determine how much time e
> Two stones, one with twice the mass of the other, are thrown straight up and rise to the same height h. Compare their changes in gravitational potential energy (choose one): (a) They rise to the same height, so the stone with twice the mass has twice the
> A 70 - kg base runner begins his slide into second base when he is moving at a speed of 4.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. (a) How much mechanical e
> An object of mass m moves to the right with a speed υ. It collides head-on with an object of mass 3m moving with speed υ/3 in the opposite direction. If the two objects stick together, what is the speed of the combined object, of mass 4m, after the colli
> For each of the situations given, state whether frictional forces do positive, negative, or zero work on the italicized object. (a) A plate slides across a table and is brought to rest by friction. (b) A person pushes a chair at constant speed across a r
> A 65.0 - kg runner has a speed of 5.20 m/s at one instant during a long - distance event. (a) What is the runner’s kinetic energy at this instant? (b) How much net work is required to double his speed?
> The driver of a car slams on her brakes to avoid colliding with a deer crossing the highway. What happens to the car’s kinetic energy as it comes to rest?
> A mechanic pushes a 2.50 x 103- kg car from rest to a speed of υ, doing 5.00 x 103 J of work in the process. During this time, the car moves 25.0 m. Neglecting friction between car and road, find (a) υ and (b) The horizontal force exerted on the car.
> Discuss whether any work is being done by each of the following agents and, if so, whether the work is positive or negative: (a) A chicken scratching the ground, (b) A person studying, (c) A crane lifting a bucket of concrete, (d) The force of gravity on
> Drops of rain fall perpendicular to the roof of a parked car during a rainstorm. The drops strike the roof with a speed of 12 m/s, and the mass of rain per second striking the roof is 0.035 kg/s. (a) Assuming the drops come to rest after striking the roo
> A 0.280-kg volleyball approaches a player horizontally with a speed of 15.0 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s. (a) What impulse is delivered to the ball by the pl
> A pitcher claims he can throw a 0.145-kg baseball with as much momentum as a 3.00-g bullet moving with a speed of 1.50 x 103 m/s. (a) What must the baseball’s speed be if the pitcher’s claim is valid? (b) Which has greater kinetic energy, the ball or the
> A high-speed photograph of a club hitting a golf ball is shown in Figure 6.3. The club was in contact with a ball, initially at rest, for about 0.0020 s. If the ball has a mass of 55 g and leaves the head of the club with a speed of 2.0 x 102 ft/s, find
> Calculate the magnitude of the linear momentum for the following cases: (a) A proton with mass equal to 1.67 x 10-27 kg, moving with a speed of 5.00 x 106 m/s; (b) A 15.0-g bullet moving with a speed of 300 m/s; (c) A 75.0-kg sprinter running with a spee
> Three ice skaters meet at the center of a rink and each stands at rest facing the center, within arm’s reach of the other two. On a signal, each skater pushes himself away from the other two across the frictionless ice. After the push, skater A with mass
> An astronaut in her space suit has a total mass of 87.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she’s on a spacewalk. Initially at rest with respect to her spacecraft, she throws
> Two objects of masses m1 = 0.56 kg and m2 = 0.88 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k = 280 N/m is placed between them as in Figure P6.28a. Neglect the mass of the spring. The spring is not attach
> A 65.0 - kg person throws a 0.045 0 - kg snowball forward with a ground speed of 30.0 m/s. A second person, with a mass of 60.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.50 m/s, an
> A 75 - kg fisherman in a 125 - kg boat throws a package of mass m = 15 kg horizontally toward the right with a speed of Ï…i = 4.5 m/s as in Figure P6.26. Neglecting water resistance, and assuming the boat is at rest before the package is thrown
> A tension force of 175 N inclined at 20.0° above the horizontal is used to pull a 40.0 - kg packing crate a distance of 6.00 m on a rough surface. If the crate moves at a constant speed, find (a) The work done by the tension force and (b) The coefficient
> Squids are the fastest marine invertebrates, using a powerful set of muscles to take in and then eject water in a form of jet propulsion that can propel them to speeds of over 11.5 m/s. What speed would a stationary 1.50 - kg squid achieve by ejecting 0.
> A girl of mass mG is standing on a plank of mass mP. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity υGP to the right relative to the plank. (The s
> A 45.0 - kg girl is standing on a 150. - kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.50 m/s to the right relative t
> A rifle with a weight of 30.0 N fires a 5.00 - g bullet with a speed of 3.00 x 102 m/s. (a) Find the recoil speed of the rifle. (b) If a 7.00 x 102 - N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.
> High - speed stroboscopic photographs show that the head of a 2.00 x 102 - g golf club is traveling at 55.0 m/s just before it strikes a 46.0 - g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 40.0 m/s.
> A pitcher throws a 0.14-kg baseball toward the batter so that it crosses home plate horizontally and has a speed of 42 m/s just before it makes contact with the bat. The batter then hits the ball straight back at the pitcher with a speed of 48 m/s. Assum
> The front 1.20 m of a 1400-kg car is designed as a “crumple zone” that collapses to absorb the shock of a collision. If a car traveling 25.0 m/s stops uniformly in 1.20 m, (a) How long does the collision last, (b) What is the magnitude of the average for
> A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at an angle of θ = 60.0° with the plane of the wall. It bounces off the wall with the same speed and angle (Fig. P6.18). If the ball is in contact with the wall for 0.200 s,
> The forces shown in the force vs. time diagram in Figure P6.17 act on a 1.5 - kg particle. Find (a) The impulse for the interval from t = 0 to t = 3.0 s and (b) The impulse for the interval from t = 0 to t = 5.0 s. If the forces act on a 1.5 - kg particl
> A force of magnitude Fx acting in the x - direction on a 2.00 - kg particle varies in time as shown in Figure P6.16. Find (a) The impulse of the force, (b) The final velocity of the particle if it is initially at rest, and (c) The final velocity of the p
> A bowling ball is suspended from the ceiling of a lecture hall by a strong cord. The ball is drawn away from its equilibrium position and released from rest at the tip of the demonstrator’s nose, as shown in Figure CQ5.6. (a) If the dem
> The force shown in the force vs. time diagram in Figure P6.15 acts on a 1.5-kg object. Find (a) The impulse of the force, (b) The final velocity of the object if it is initially at rest, and (c) The final velocity of the object if it is initially moving
> A 65.0-kg basketball player jumps vertically and leaves the floor with a velocity of 1.80 m/s upward. (a) What impulse does the player experience? (b) What force does the floor exert on the player before the jump? (c) What is the total average force exer
> A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing its speed from 0 to 5.20 m/s in 0.832 s. What are the magnitudes of (a) The linear impulse and (b) The average total force experienced by a 70.0-kg passeng
> A tennis player receives a shot with the ball (0.060 0 kg) traveling horizontally at 50.0 m/s and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite direction. (a) What is the impulse delivered to the ball by the racket? (b
> A ball of mass 0.150 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.960 m. What impulse was given to the ball by the floor?
> A man claims he can safely hold on to a 12.0-kg child in a head-on collision with a relative speed of 120-mi/h lasting for 0.10 s as long as he has his seat belt on. (a) Find the magnitude of the average force needed to hold onto the child. (b) Based on
> A soccer player takes a corner kick, lofting a stationary ball 35.0° above the horizon at 22.5 m/s. If the soccer ball has a mass of 0.425 kg and the player’s foot is in contact with it for 5.00 x 10-2 s, find (a) The x - and y - components of the soccer
> An estimated force vs. time curve for a baseball struck by a bat is shown in Figure P6.8. From this curve, determine (a) The impulse delivered to the ball and (b) The average force exerted on the ball. Figure P6.8:
> An object has a kinetic energy of 275 J and a momentum of magnitude 25.0 kg ? m/s. Find the (a) Speed and (b) Mass of the object.
> (a) If two automobiles collide, they usually do not stick together. Does this mean the collision is elastic? (b) Explain why a head-on collision is likely to be more dangerous than other types of collisions.
> Starting from rest, a 5.00 - kg block slides 2.50 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is µk 5 0.436. Determine (a) The work done by the force of gravity, (b) The work done by the friction fo
> A skater is standing still on a frictionless ice rink. Her friend throws a Frisbee straight to her. In which of the following cases is the largest momentum transferred to the skater? (a) The skater catches the Frisbee and holds onto it. (b) The skater ca
> Two identical ice hockey pucks, labeled A and B, are sliding towards each other at speed Ï…. Which one of the following statements is true concerning their momenta and kinetic energies?
> If two objects collide and one is initially at rest, (a) Is it possible for both to be at rest after the collision? (b) Is it possible for only one to be at rest after the collision? Explain.
> Two particles of different mass start from rest. The same net force acts on both of them as they move over equal distances. How do their final kinetic energies compare? (a) The particle of larger mass has more kinetic energy. (b) The particle of smaller
> Does a larger net force always produce a larger change in kinetic energy than a smaller net force? Explain.
> An open box slides with constant speed across the frictionless surface of a frozen lake. If water from a rain shower falls vertically downward into it, does the box: (a) Speed up, (b) Slow down, or (c) Continue to move with constant speed?
> An air bag inflates when a collision occurs, protecting a passenger (the dummy in Figure CQ6.12) from serious injury. Why does the air bag soften the blow? Discuss the physics involved in this dramatic photograph. Figure CQ6.12:
> Two carts move in the same direction along a frictionless air track, each acted on by the same constant force for a time interval Δt. Cart 2 has twice the mass of cart 1. Which one of the following statements is true? (a) Each cart has the same change in
> Bob, of mass m, drops from a tree limb at the same time that Esther, also of mass m, begins her descent down a frictionless slide. If they both start at the same height above the ground, which of the following is true about their kinetic energies as they
> Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal, as in Figure 5.16. Negle
> (a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.
> A block slides at constant speed down a ramp while acted on by three forces: its weight, the normal force, and kinetic friction. Respond to each statement, true or false. (a) The combined net work done by all three forces on the block equals zero. (b) Ea
> In Figure 5.5 (a)–(d), a block moves to the right in the positive x - direction through the displacement Δx( while under the influence of a force with the same magnitude F(. Which of the following is the correct order of the
> A book of mass m is projected with a speed υ across a horizontal surface. The book slides until it stops due to the friction force between the book and the surface. The surface is now tilted 30°, and the book is projected up the surface with the same ini
> Elastic potential energy depends on the spring constant and the distance the spring is stretched or compressed. By what factor does the elastic potential energy change if the spring’s stretch is (a) Doubled or (b) Tripled?
> True or False: The elastic potential energy of a stretched or compressed spring is always positive.
> Calculate the elastic potential energy of a spring with spring constant k = 225 N/m that is (a) Compressed and (b) Stretched by 1.00 x 10-2 m.
