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physics
mechanics
College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions
If a spring is compressed 2.0 cm from its equilibrium position and then compressed an additional 2.0 cm, how much more work is done in the second compression than in the first? Explain.
You want to decrease the kinetic energy of an object as much as you can. You can do so by either reducing the mass by half or reducing the speed by half. Which option should you pick, and why?
A certain amount of work W is required to accelerate a car from rest to a speed v. How much work is required to accelerate the car from rest to a speed of v/2?
If a person does 50 J of work in moving a 30-kg box over a 10-m distance on a horizontal surface, what is the minimum force required?
A crate is dragged 3.0 m along a rough floor with a constant velocity by a worker applying a force of 500 N to a rope at an angle of to the horizontal. (a) How many forces are acting on the crate? (b) How much work does each of these forces do? (c) What is the total work done on the crate?
A hot-air balloon ascends at a constant rate. (a) The weight of the balloon does (1) positive work, (2) negative work, (3) no work. Why? (b) A hot-air balloon with a mass of 500 kg ascends at a constant rate of 1.50 m/s for 20.0s. How much work is done by the upward buoyant force? (Neglect air
A hockey puck with a mass of 200 g and an initial speed of 25.0 m/s slides freely to rest in the space of 100 m on a sheet of horizontal ice. How many forces do nonzero work on it as it slows: (a) (1) none, (2) one, (3) two, or (4) three? Explain. (b) Determine the work done by all the individual
An eraser with a mass of 100 g sits on a book at rest. The eraser is initially 10.0 cm from any edge of the book. The book is suddenly yanked very hard and slides out from under the eraser. In doing so, it partially drags the eraser with it, although not enough to stay on the book. The coefficient
A500-kg, light-weight helicopter ascends from the ground with an acceleration of 2.00 m/s2. Over a 5.00-s interval, what is (a) The work done by the lifting force, (b) The work done by the gravitational force, and (c) The net work done on the helicopter?
A man pushes horizontally on a desk that rests on a rough wooden floor. The coefficient of static friction between the desk and floor is 0.750 and the coefficient of kinetic friction is 0.600. The desk’s mass is 100 kg. He pushes just hard enough to get the desk moving and continues pushing with
A student could either pull or push, at an angle of from the horizontal, a 50-kg crate on a horizontal surface, where the coefficient of kinetic friction between the crate and surface is 0.20. The crate is to be moved a horizontal distance of 15 m. (a) Compared with pushing, pulling requires the
To measure the spring constant of a certain spring, a student applies a 4.0-N force, and the spring stretches by 5.0 cm. What is the spring constant?
A spring has a spring constant of 30 N/m. How much work is required to stretch the spring 2.0 cm from its equilibrium position?
If it takes 400 J of work to stretch a spring 8.00 cm, what is the spring constant?
A 5.0-kg box slides a 10-m distance on ice. If the coefficient of kinetic friction is 0.20, what is the work done by the friction force?
If a 10-N force is used to compress a spring with a spring constant of 4.0 x 102 N/m, what is the resulting spring compression?
A certain amount of work is required to stretch a spring from its equilibrium position. (a) If twice the work is performed on the spring, the spring will stretch more by a factor of (1) √2 (2) 2, (3) 1√2 (4) 1/2. Why? (b) If 100 J of work is done to pull a spring 1.0 cm, what work is required
Compute the work done by the variable force in the graph of F versus x in Fig. 5.29.
A spring with a force constant of is to be stretched from 0 to 20 cm. (a) The work required to stretch the spring from 10 cm to 20 cm is (1) more than, (2) the same as, (3) less than that required to stretch it from 0 to 10 cm. (b) Compare the two work values to prove your answer to part (a).
In gravity-free interstellar space, a spaceship fires its rockets to speed up. The rockets are programmed to increase thrust from zero to 1.00 x 104 N with a linear increase over the course of 18.0 km. Then the thrust decreases linearly back to zero over the next 18.0 km. Assuming the rocket was
A particular spring has a force constant of 2.5 x 103 N/m. (a) How much work is done in stretching the relaxed spring by 6.0 cm? (b) How much more work is done in stretching the spring an additional 2.0 cm?
For the spring in Exercise 25, how much mass would have to be suspended from the vertical spring to stretch it In exercise A particular spring has a force constant of 2.5 x 103 N/m. (a) The first 6.0 cm and (b) The additional 2.0 cm?
In stretching a spring in an experiment, a student inadvertently stretches it past its elastic limit; the force-versus-stretch graph is shown in Fig. 5.30. Basically, after it reaches its limit, the spring begins to behave as if it were considerably stiffer. How much work was done on the spring?
A spring (spring 1) with a spring constant of is attached to a wall and connected to another weaker spring (spring 2) with a spring constant of on a horizontal surface. Then an external force of 100 N is applied to the end of the weaker spring (#2). How much potential energy is stored in each
A 0.20-kg object with a horizontal speed of hits a wall and bounces directly back with only half the original speed. (a) What percentage of the object’s initial kinetic energy is lost: (1) 25%, (2) 50%, or (3) 75%? (b) How much kinetic energy is lost in the ball’s collision with the wall?
A 1200-kg automobile travels at 90 km/h. (a) What is its kinetic energy? (b) What net work would be required to bring it to a stop?
A constant net force of 75 N acts on an object initially at rest as it moves through a parallel distance of 0.60 m. (a) What is the final kinetic energy of the object? (b) If the object has a mass of 0.20 kg, what is its final speed?
A 2.00-kg mass is attached to a vertical spring with a spring constant of 250 N/m. A student pushes on the mass vertically upward with her hand while slowly lowering it to its equilibrium position. (a) How many forces do nonzero work on the object: (1) one, (2) two, or (3) three? Explain your
The stopping distance of a vehicle is an important safety factor. Assuming a constant braking force, use the work–energy theorem to show that a vehicle’s stopping distance is proportional to the square of its initial speed. If an automobile traveling at is brought to a stop in 50 m, what would
A large car of mass 2m travels at speed v. A small car of mass m travels with a speed 2v. Both skid to a stop with the same coefficient of friction. (a) The small car will have (1) a longer, (2) the same, (3) a shorter stopping distance. (b) Calculate the ratio of the stopping distance of the
An out-of-control truck with a mass of 5000 kg is traveling at (about 80 mi/h) when it starts descending a steep (15o) incline. The incline is icy, so the coefficient of friction is only 0.30. Use the work– energy theorem to determine how far the truck will skid (assuming it locks its brakes and
If the work required to speed up a car from 10 km/h to 20 km/h is 5.0 x 103 J, what would be the work required to increase the car’s speed from 20 km/h to 30 km/h?
How much more gravitational potential energy does a 1.0-kg hammer have when it is on a shelf 1.2 m high than when it is on a shelf 0.90 m high?
You are told that the gravitational potential energy of a 2.0-kg object has decreased by 10 J. (a) With this information, you can determine (1) the object’s initial height, (2) the object’s final height, (3) both the initial and the final height, (4) only the difference between the two
Six identical books, 4.0 cm thick and each with a mass of 0.80 kg, lie individually on a flat table. How much work would be needed to stack the books one on top of the other?
A 3.00-kg block slides down a frictionless plane inclined to the horizontal. If the length of the plane’s surface is 1.50 m, how much work is done, and by what force?
The floor of the basement of a house is 3.0 m below ground level, and the floor of the attic is 4.5 m above ground level. (a) If an object in the attic were brought to the basement, the change in potential energy will be greatest relative to which floor: (1) attic, (2) ground, (3) basement, or (4)
A 0.50-kg mass is placed on the end of a vertical spring that has a spring constant of 75 N/m and eased down into its equilibrium position. (a) Determine the change in spring (elastic) potential energy of the system. (b) Determine the system’s change in gravitational potential energy.
A horizontal spring, resting on a frictionless tabletop, is stretched 15 cm from its unstretched configuration and a 1.00-kg mass is attached to it. The system is released from rest. A fraction of a second later, the spring finds itself compressed 3.0 cm from its unstretched configuration. How does
A student has six textbooks, each with a thickness of 4.0 cm and a weight of 30 N. What is the minimum work the student would have to do to place all the books in a single vertical stack, starting with all the books on the surface of the table?
A 1.50-kg mass is placed on the end of a spring that has a spring constant of 175 N/m. The mass€“ spring sys-tem rests on a frictionless incline that is at an angle of from the horizontal (Fig. 5.31). The system is eased into its equilibrium position, where it stays.(a) Determine the
A 0.300-kg ball is thrown vertically upward with an initial speed of 10.0 m/s. If the initial potential energy is taken as zero, find the ball’s kinetic, potential, and mechanical energies (a) At its initial position, (b) At 2.50m above the initial position, and (c) At its maximum height.
What is the maximum height reached by the ball in Exercise 45? In exercise A 0.300-kg ball is thrown vertically upward with an initial speed of 10.0 m/s. If the initial potential energy is taken as zero, find the ball’s kinetic, potential, and mechanical energies
Referring to Fig. 3.13, find the speed with which the stone strikes the water using energy considerations.
A girl swings back and forth on a swing with ropes that are 4.00 m long. The maximum height she reaches is 2.00 m above the ground. At the lowest point of the swing, she is 0.500 m above the ground. (a) The girl attains the maximum speed (1) at the top, (2) in the middle, (3) at the bottom of the
A 1.00-kg block (M) is on a flat frictionless surface (Fig. 5.32). This block is attached to a spring initially at its relaxed length (spring constant is 50.0 N/m). Alight string is attached to the block and runs over a frictionless pulley to a 450-g dangling mass (m). If the dangling mass is
Suppose the coefficient of kinetic friction between the block and the plane in Exercise 4 is 0.275. What would be the net work done in this case? In exercise A 3.00-kg block slides down a frictionless plane inclined to the horizontal. If the length of the plane’s surface is 1.50 m, how much work
A 500-g (small) mass on the end of a 1.50-m-long string is pulled aside from the vertical and shoved downward (toward the bottom of its motion) with a speed of 2.00 m/s. (a) Is the angle on the other side (1) greater than, (2) less than, or (3) the same as the angle on the initial side (15o)?
A 0.20-kg rubber ball is dropped from a height of 1.0 m above the floor and it bounces back to a height of 0.70 m. (a) What is the ball’s speed just before hitting the floor? (b) What is the speed of the ball just as it leaves the ground? (c) How much energy was lost and where did it go?
A skier coasts down a very smooth, 10-m-high slope similar to the one shown in Fig. 5.21. If the speed of the skier on the top of the slope is 5.0 m/s, what is his speed at the bottom of the slope?
A roller coaster travels on a frictionless track as shown in Fig. 5.33.(a) If the speed of the roller coaster at point A is 5.0 m/s, what is its speed at point B? (b) Will it reach point C? (c) What minimum speed at point A is required for the roller coaster to reach point C?
A simple pendulum has a length of 0.75 m and a bob with a mass of 0.15 kg. The bob is released from an angle of relative to a vertical reference line (Fig. 5.34).(a) Show that the vertical height of the bob when it is released is h = L (1 €“ cos 25o). (b) What is the kinetic energy of
Suppose the simple pendulum in Exercise 54 were released from an angle of 60o.In Exercise A simple pendulum has a length of 0.75 m and a bob with a mass of 0.15 kg. The bob is released from an angle of relative to a vertical reference line (Fig. 5.34).(a) What would be the speed of the bob at the
A 1.5-kg box that is sliding on a frictionless surface with a speed of approaches a horizontal spring. (See Fig. 5.19.) The spring has a spring constant of 2000 N/m. If one end of the spring is fixed and the other end changes its position, (a) How far will the spring be compressed in stopping the
A 0.50-kg mass is suspended on a spring that stretches 3.0 cm. (a) What is the spring constant? (b) What added mass would stretch the spring an additional 2.0 cm? (c) What is the change in potential energy when the mass is added?
A vertical spring with a force constant of is compressed 6.0 cm and a 0.25-kg ball placed on top. The spring is released and the ball flies vertically upward. How high does the ball go?
A block with a mass m1 = 6.0 kg sitting on a friction-less table is connected to a suspended mass m2 = 2.0 by a light string passing over a frictionless pulley. Using energy considerations, find the speed at which m2 hits the floor after descending 0.75 m.
A father pulls his young daughter on a sled with a constant velocity on a level surface a distance of 10 m, as illustrated in Fig. 5.27a. If the total mass of the sled and the girl is 35 kg and the coefficient of kinetic friction between the sled runners and the snow is 0.20, how much work does the
A hiker plans to swing on a rope across a ravine in the mountains, as illustrated in Fig. 5.35, and to drop when she is just above the far edge.(a) At what horizontal speed should she be moving when she starts to swing? (b) Below what speed would she be in danger of falling into the ravine?
In Exercise 52, if the skier has a mass of 60 kg and the force of friction retards his motion by doing 2500 J of work, what is his speed at the bottom of the slope?In exercise A skier coasts down a very smooth, 10-m-high slope similar to the one shown in Fig. 5.21. If the speed of the skier on the
A 1.00-kg block (M) is on a frictionless, 20o inclined plane. The block is attached to a spring (k = 25 N/m) that is fixed to a wall at the bottom of the incline. Alight string attached to the block runs over a frictionless pulley to a 40.0-g suspended mass. The suspended mass is given an initial
A girl consumes 8.4 x 106J (2000 food calories) of energy per day while maintaining a constant weight. What is the average power she produces in a day?
A 1500-kg race car can go from 0 to 90 km/h in 5.0 s. What average power is required to do this?
The two 0.50-kg weights of a cuckoo clock descend 1.5 m in a three-day period. At what rate is their total gravitational potential energy decreased?
A pump lifts 200 kg of water per hour a height of 5.0 m. What is the minimum necessary power output rating of the water pump in watts and horsepower?
A race car is driven at a constant velocity of on a straight, level track. The power delivered to the wheels is 150 kW. What is the total resistive force on the car?
An electric motor with a 2.0-hp output drives a machine with an efficiency of 40%. What is the energy output of the machine per second?
Water is lifted out of a well 30.0 m deep by a motor rated at 1.00 hp. Assuming 90% efficiency, how many kilograms of water can be lifted in 1 min?
A father pushes horizontally on his daughter€™s sled to move it up a snowy incline, as illustrated in Fig. 5.27b. If the sled moves up the hill with a constant velocity, how much work is done by the father in moving it from the bottom to the top of the hill? (Some necessary data are given
How much power must you exert to horizontally drag a 25.0-kg table 10.0 m across a brick floor in 30.0 s at constant velocity, assuming the coefficient of kinetic friction between the table and floor is 0.550?
A 3250-kg aircraft takes 12.5 min to achieve its cruising altitude of 10.0 km and cruising speed of 850 km/h. If the plane’s engines deliver, on average, 1500 hp during this time, what is the efficiency of the engines?
A sleigh and driver with a total mass of 120 kg are pulled up a hill with a incline by a horse, as illustrated in Fig. 5.36.(a) If the overall retarding frictional force is 950 N and the sled moves up the hill with a constant velocity of 5.0 km/h, what is the power output of the horse? (Express in
A construction hoist exerts an upward force of 500 N on an object with a mass of 50 kg. If the hoist started from rest, determine the power it expended to lift the object vertically for 10 s under these conditions.
Two identical springs (neglect their masses) are used to €œplay catch€ with a small block of mass 100 g (Fig. 5.37). Spring A is attached to the floor and compressed 10.0 cm with the mass on the end of it (loosely). Spring A is released from rest and the mass is accelerated
A 200-g ball is launched from a height of 20.0 m above a lake. Its launch angle is 40o and it has an initial kinetic energy of 90.0 J. (a) Use energy methods to determine its maximum height above the lake surface. (b) Use projectile motion kinematics to repeat part (a). (c) Use energy methods to
A 1.20-kg ball is projected straight upward with an initial speed of 18.5 m/s and reaches a maximum height of 14.7 m. (a) Show numerically that total mechanical energy is not conserved during this part of the ball’s motion. (b) Determine the work done on the ball by the force of air resistance.
An ideal spring of force constant k is hung vertically from the ceiling, and a held object of mass m is attached to the loose end. You carefully and slowly ease that mass down to its equilibrium position by keeping your hand under it until it reaches that position. (a) Show that the spring’s
A winch is capable of hauling a ton of bricks vertically two stories (6.25 m) in 19.5 s. If the winch’s motor is rated at 5.00 hp, determine its efficiency during raising the load.
A0.455-kg soccer ball is kicked off level ground at an angle of 40o with an initial speed of 30.0 m/s. Neglecting air resistance, (a) At its maximum height off the ground, its kinetic energy will be (1) less than its value at launch, but not zero, (2) more than its value at launch, (3) zero.
A block on a level frictionless surface has two horizontal forces applied, as shown in Fig. 5.28.(a) What force F2 would cause the block to move in a straight line to the right? (b) If the block moves 50 cm, how much work is done by each force? (c) What is the total work done by the two forces?
A stationary object receives a direct hit by another object moving toward it. Is it possible for both objects to be at rest after the collision? Explain.
Does the conservation of momentum follow from Newton’s third law?
Since K = p2/2m, how can kinetic energy be lost in an inelastic collision while the total momentum is still con-served? Explain.
Can all of the kinetic energy be lost in the collision of two objects? Explain.
Automobiles used to have firm steel bumpers for safety. Today auto bumpers are made out of materials that crumple or collapse on sufficient impact. Why is this?
Two balls of equal mass collide head on in a completely inelastic collision and come to rest. (a) Is the kinetic energy conserved? (b) Is the momentum conserved? Explain.
Rockets used in the space program are generally multistage— that is, they have stacked stages, each with its own engine and propellant. Starting with the bottom, the stages are jettisoned when they have run out of fuel. The first stage is usually the largest, the second stage above it is the next
Two objects have the same momentum. Do they necessarily have the same kinetic energy? Explain.
Two objects have the same kinetic energy. Do they necessarily have the same momentum? Explain.
A karate student tries not to follow through in order to break a board, as shown in Fig. 6.27. How can the abrupt stop of the hand (with no follow- through) generate so much force?
Explain the difference for each of the following pairs of actions in terms of impulse: (a) A golfer’s long drive and a short chip shot; (b) A boxer’s jab and a knockout punch; (c) A baseball player’s bunting action and a home- run swing.
When jumping from a height to the ground, it is advised to land with the legs bent rather than stiff- legged. Why is this?
In the Revolutionary War, the Americans had an advantage in using long rifles, instead of the smooth bore muskets used by the British. The long rifle had a barrel of 48 in. or more, whereas the musket barrel length was on the order of 30 in. (Fig. 6.28). The long rifle had a much greater range than
An airboat of the type used in swampy and marshy areas is shown in Fig. 6.29. Explain the principle of its propulsion. Using the concept of conservation of linear momentum, determine what would happen to the boat if a sail were installed behind the fan.
If a 60-kg woman is riding in a car traveling at 90 km/h, what is her linear momentum relative to (a) The ground and (b) The car?
Two runners of mass 70 kg and 60 kg, respectively, have a total linear momentum of 350 kg ∙ m/s. The heavier runner is running at 2.0 m/s. Determine the possible velocities of the lighter runner.
A 0.20-kg billiard ball traveling at a speed of strikes the side rail of a pool table at an angle of (Fig. 6.31). If the ball rebounds at the same speed and angle, what is the change in its momentum?
Suppose the billiard ball in Fig. 6.31 approaches the rail at a speed of and an angle of 60o, as shown, but rebounds at a speed of 10 m/s and an angle of 50o. What is the change in momentum in this case?
A loaded tractor-trailer with a total mass of 5000 kg traveling at hits a loading dock and comes to a stop in 0.64 s. What is the magnitude of the average force exerted on the truck by the dock?
A 2.0-kg mud ball drops from rest at a height of 15 m. If the impact between the ball and the ground lasts 0.50 s, what is the average net force exerted by the ball on the ground?
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