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 associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool.
(c) Determine her initial speed Ï
0 at the launch point in terms of g and h.
(d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, Ï
(e) Use the x - component of the answer to part (c) to eliminate Ï
0 from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle Î¸.
(f) Would your answers be the same if the waterslide were not frictionless? Explain. Figure P5.46:
> A 62.0 - kg cheetah accelerates from rest to its top speed of 32.0 m/s. (a) How much network is required for the cheetah to reach its top speed? (b) One food Calorie equals 4186 J. How many Calories of network are required for the cheetah to reach its to
> A worker pushing a 35.0 - kg wooden crate at a constant speed for 12.0 m along a wood floor does 350 J of work by applying a constant horizontal force of magnitude F0 on the crate. (a) Determine the value of F0. (b) If the worker now applies a force grea
> A 7.00 - kg bowling ball moves at 3.00 m/s. How fast must a 2.45 - g Ping - Pong ball move so that the two balls have the same kinetic energy?
> A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle Î¸ = 25.0Â° below the horizontal as shown in Figure P5.8. Det
> A horizontal force of 150 N is used to push a 40.0 - kg packing crate a distance of 6.00 m on a rough horizontal surface. If the crate moves at constant speed, find (a) The work done by the 150 - N force and (b) The coefficient of kinetic friction betwee
> A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25° below the horizontal. The force is just sufficient to overcome various frictional forces, so the cart moves at constant speed. (a) Find the work done by the shopper
> Two blocks, A and B (with mass 50.0 kg and 1.00 x 102 kg, respectively), are connected by a string, as shown in Figure P5.86. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between block A and the incline is Â
> Three objects with masses m1 = 5.00 kg, m2 = 10.0 kg, and m3 = 15.0 kg, respectively, are attached by strings over frictionless pulleys as indicated in Figure P5.85. The horizontal surface exerts a force of friction of 30.0 N on m2. If the system is rele
> A cat plays with a toy mouse suspended from a light string of length 1.25 m, rapidly batting the mouse so that it acquires a speed of 2.75 m/s while the string is still vertical. Use energy conservation to find the mouse’s maximum height above its origin
> A loaded ore car has a mass of 9.50 x 102 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0° above the horizontal. The car accelerates uniforml
> Choose the best answer. A car traveling at constant speed has a net work of zero done on it. (a) True (b) False (c) The answer depends on the motion.
> As a 75.0 - kg man steps onto a bathroom scale, the spring inside the scale compresses by 0.650 mm. Excited to see that he has lost 2.50 kg since his previous weigh - in, the man jumps 0.300 m straight up into the air and lands directly on the scale. (a)
> A truck travels uphill with constant velocity on a highway with a 7.0° slope. A 50. - kg package sits on the floor of the back of the truck and does not slide, due to a static frictional force. During an interval in which the truck travels 340 m, (a) Wha
> Apollo 14 astronaut Alan Shepard famously took two golf shots on the Moon where it’s been estimated that an expertly hit shot could travel for 70.0 s through the Moon’s reduced gravity, airless environment to a maximum range of 4.00 km (about 2.5 miles).
> In the dangerous “sport” of bungee jumping, a daring student jumps from a hot air balloon with a specially designed elastic cord attached to his waist. The unstretched length of the cord is 25.0 m, the student weighs 7.00 x 102 N, and the balloon is 36.0
> A hummingbird hovers by exerting a downward force on the air equal, on average, to its weight. By Newton’s third law, the air exerts an upward force of the same magnitude on the bird’s wings. Find the average mechanical power delivered by a 3.00 - g humm
> A childâ€™s pogo stick (Fig. P5.77) stores energy in a spring (k = 2.50 x 104 N/m). At position â’¶ (x1 = -0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position â’&middo
> A 5.0 - kg block is pushed 3.0 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of Î¸ = 30Â° with the horizontal, as shown in Figure P5.76. If the coefficient of kinetic friction betwee
> A ski jumper starts from rest 50.0 m above the ground on a frictionless track and flies off the track at an angle of 45.0° above the horizontal and at a height of 10.0 m above the level ground. Neglect air resistance. (a) What is her speed when she leave
> A 50.0 - kg student evaluates a weight loss program by calculating the number of times she would need to climb a 12.0 - m high flight of steps in order to lose one pound (0.45 kg) of fat. Metabolizing 1.00 kg of fat can release 3.77 x 107 J of chemical e
> In terms of saving energy, bicycling and walking are far more efficient means of transportation than is travel by automobile. For example, when riding at 10.0 mi/h, a cyclist uses food energy at a rate of about 400 kcal/h above what he would use if he we
> A weightlifter lifts a 350-N set of weights from ground level to a position over his head, a vertical distance of 2.00 m. How much work does the weightlifter do, assuming he moves the weights at constant speed?
> The particle described in Problem 71 (Fig. P5.71) is released from point A at rest. Its speed at B is 1.50 m/s. (a) What is its kinetic energy at B? (b) How much mechanical energy is lost as a result of friction as the particle goes from A to B? (c) Is i
> A 2.00 x 102 - g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R = 30.0 cm (Fig. P5.71). Calculate (a) Its gravitational potential energy at A relative to B, (b) Its kinetic energy at B, (c) Its speed at
> A 3.50 - kN piano is lifted by three workers at constant speed to an apartment 25.0 m above the street using a pulley system fastened to the roof of the building. Each worker is able to deliver 165 W of power, and the pulley system is 75% efficient (so t
> Two objects (m1 = 5.00 kg and m2 = 3.00 kg) are connected by a light string passing over a light, frictionless pulley as in Figure P5.69. The 5.00 - kg object is released from rest at a point h = 4.00 m above the table. (a) Determine the speed of each ob
> A toy gun uses a spring to project a 5.3 - g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 15 cm long, and a constant frictional force of 0.032 N exists between barrel and projectile. With what speed does the p
> (a) A 75 - kg man steps out a window and falls (from rest) 1.0 m to a sidewalk. What is his speed just before his feet strike the pavement? (b) If the man falls with his knees and ankles locked, the only cushion for his fall is an approximately 0.50 - cm
> A block of mass 12.0 kg slides from rest down a frictionless 35.0° incline and is stopped by a strong spring with k = 3.00 x 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block
> 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 does the archer do in pulling the bow?
> A ball of mass m = 1.80 kg is released from rest at a height h = 65.0 cm above a light vertical spring of force constant k as in Figure P5.64a. The ball strikes the top of the spring and compresses it a distance d = 9.00 cm as in Figure P5.64b. Neglectin
> A roller - coaster car of mass 1.50 x 103 kg is initially at the top of a rise at point Ⓐ. It then moves 35.0 m at an angle of 50.0° below the horizontal to a lower point Ⓑ. (a) Find both the potential energy of the system when the car is at points Ⓐ and
> A boy standing at one end of a floating raft that is stationary relative to the shore walks to the opposite end of the raft, away from the shore. As a consequence, the raft (a) Remains stationary, (b) Moves away from the shore, or (c) Moves toward the sh
> An outfielder throws a 0.150 - kg baseball at a speed of 40.0 m/s and an initial angle of 30.0°. What is the kinetic energy of the ball at the highest point of its motion?
> The force acting on an object is given by Fx = (8x - 16) N, where x is in meters. (a) Make a plot of this force vs. x from x = 0 to x = 3.00 m. (b) From your graph, find the net work done by the force as the object moves from x = 0 to x = 3.00 m.
> An object of mass 3.00 kg is subject to a force Fx that varies with position as in Figure P5.60. Find the work done by the force on the object as it moves (a) From x = 0 to x = 5.00 m, (b) From x = 5.00 m to x = 10.0 m, and (c) From x = 10.0 m to x = 15.
> The force acting on a particle varies as in Figure P5.59. Find the work done by the force as the particle moves (a) From x = 0 to x = 8.00 m, (b) From x = 8.00 m to x = 10.0 m, and (c) From x = 0 to x = 10.0 m. Figure P5.59:
> A 1.50 x 103 - kg car starts from rest and accelerates uniformly to 18.0 m/s in 12.0 s. Assume that air resistance remains constant at 4.00 x 102 N during this time. Find (a) The average power developed by the engine and (b) The instantaneous power outpu
> A certain rain cloud at an altitude of 1.75 km contains 3.20 x 107 kg of water vapor. How long would it take for a 2.70 - kW pump to raise the same amount of water from Earth’s surface to the cloud’s position?
> Under normal conditions the human heart converts about 13.0 J of chemical energy per second into 1.30 W of mechanical power as it pumps blood throughout the body. (a) Determine the number of Calories required to power the heart for one day, given that 1
> The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during its acceleration.
> The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during its acceleration.
> 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 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 â’¶ and slides on the frictionless track shown in Figure P5.36. Determine (a) The blockâ€™s speed at points â’· and â’¸ 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 â€œhelper springsâ€ 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.
> 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.)
> 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 sheâ€™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