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What we found:

A 75.0kg log floats downstream with a speed of 1.80 m/s. Eight frogs hop onto the log in a series of perfectly inelastic collisions. If each frog has a mass of 0.30 kg and an upstream speed of 1.3 m/s, what is the change in kinetic energy for this system?

A rocket of mass m is launched with kinetic energy K0, from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii in terms of the gravitational constant, G; the mass of the Earth, mE: the radius of the Earth, RE; and the mass of the rocket?

You kick a ball straight up. Compare the sign of the work done by gravity on the ball while it goes up with the sign of the work done by gravity while it goes down.

Jill does twice as much work as Jack does and in half the time. Jill’s power output is

A car traveling to the right with a speed v brakes to a stop in a distance d. What is the work done on the car by the frictional force F? (Assume that the frictional force is constant)

How does the time t1 of a block m reaching the bottom of slide 1 compare with t2, the time taken block of mass 2m to reach the end of slide 2 thats curved? The blocks are released from the same height.

How does the speed v1 of a block m reaching the bottom of slide 1 compare with v2, the speed of a block 2m reaching the end of slide 2? The blocks are released from the same height.

A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below if there is no significant air resistance, assuming equal initial speeds?

One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance [katex] h [/katex] above the floor. A block of mass M is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance [katex] x [/katex]. The block is released and strikes the floor a horizontal distance [katex] D [/katex] from the edge of the table. Air resistance is negligible. Derive an expressions for the following quantities only in terms of [katex] M, x, D, h, [/katex] and any constants. (a) The time elapsed from the instant the block leaves the table to the instant it strikes the floor. (b)The horizontal component of the velocity of the block just before it hits the floor. (c) The work done on the block by the spring. (d) The spring constant.

A lighter car and a heavier truck, each traveling to the right with the same speed v hit their brakes. The retarding frictional force F on both cars turns out to be constant and the same. After both vehicles travel a distance D (and both are still moving), which of the following statements is true?

A 100 kg person is riding a 10 kg bicycle up a 25° hill. The hill is long and the coefficient of static friction is 0.9. The person rides 10 m up the hill then takes a rest at the top. If she then starts from rest from the top of the hill and rolls down a distance of 7 m before squeezing hard on the brakes locking the wheels. How much work is done by friction to bring the bicycle to a full stop, knowing that the coefficient of kinetic friction is 0.65?

In which one of the following circumstances does the principle of conservation of mechanical energy apply, even though a nonconservative force acts on the moving object?

A person is making homemade ice cream. She exerts a force of magnitude 23 N on the free end of the crank handle on the ice-cream maker, and this end moves on a circular path of radius 0.25 m. The force is always applied parallel to the motion of the handle. If the handle is turned once every 1.7 s, what is the average power being expended?

An object is projected vertically upward from ground level. It rises to a maximum height H. If air resistance is negligible, which of the following must be true for the object when it is at a height H/2 ?

A child pushes horizontally on a box of mass m with constant speed v across a rough horizontal floor. The coefficient of friction between the box and the floor is µ. At what rate does the child do work on the box?

A satellite in circular orbit around the Earth moves at constant speed. This orbit is maintained by the force of gravity between the Earth and the satellite, yet no work is done on the satellite. How is this possible?

Two balls are thrown off a building with the same speed, one straight up and one at a 45° angle. Which statement is true if air resistance can be ignored?

A 0.5 kg cart, on a frictionless 2 m long table, is being pulled by a 0.1 kg mass connected by a string and hanging over a pulley. The system is released from rest. After the hanging mass falls 0.5 m, calculate the speed of the cart on the table. Use ONLY forces and energy.

The box in the diagram is sliding to the right across a horizontal table, under the influence of the forces shown. Which force(s) is doing negative work on the box?

Two blocks of ice, one five times as heavy as the other, are at rest on a frozen lake. A person then pushes each block the same distance d. Ignore friction and assume that an equal force F is exerted on each block. Which of the following statements is true about the kinetic energy of the heavier block after the push?

An object with a mass m = 80 g is attached to a spring with a force constant k = 25 N/m. The spring is stretched 52.0 cm and released from rest. If it is oscillating on a horizontal frictionless surface, determine the velocity of the mass when it is halfway to the equilibrium position.

You are working out on a rowing machine. Each time you pull the rowing bar toward you, it moves a distance of 1.25 m in a time of 0.84 s. The readout on the display indicates that the average power you are producing is 76 W. What is the magnitude of the force that you exert on the handle?

In 3.0 minutes, a ski lift raises 10 skiers at constant speed to a height of 85 m. The average mass of each skier is 67.5 kg. What is the average power provided by the tension in the cable pulling the lift?

A crate is pulled 2.5 m at constant velocity along a 25° incline. The coefficient of kinetic friction between the crate and the plane is 0.250. What is the efficiency of this procedure?

The efficiency of a pulley system is 55%. The pulleys are used to raise a mass of 90.0 kg to a height of 5.60 m. What force is exerted on the rope of the pulley system if the rope is pulled for 22 m in order to raise the mass to the required height?

An object at rest suddenly explodes into two fragments by an explosion. One fragment acquires 3 times the kinetic energy of the other. What is the ratio of their masses?

Refer to the diagram above and solve all equations in-terms of R, M, k, and constants. What is the speed mass 2M as it reaches point B? Calculate the tension in the string supporting mass 2M as it reaches point B. Mass 2M collides with a smaller mass M at point B. After the collision, mass 2M has a speed equal to 1/3 its original value before the collision. What is the speed of mass M after the collision? Mass M then moves along the ground without friction with the speed found in #3 above, until it collides with the spring. Determine the maximum compression of the spring at C.

A 0.0350 kg bullet moving horizontally at 425 m/s embeds itself into an initially stationary 0.550 kg block. What is their velocity just after the collision? The bullet-embedded block slides on horizontal surface with a 0.40 kinetic coefficient of friction. What is its velocity after sliding 10.0 meters? The bullet-embedded block then strikes and sticks to a stationary 2.50 kg block (at the 10.0 m point). How far does system travel before stopping?

A ball is thrown straight up. At what point does the ball have the most energy?

A block of mass 3.0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium. The 3.0 kg block is then taken off and the spring returns to its original height. Now a 4.0 kg block is placed on the spring and released from rest. How far will the 4.0 kg block fall before its direction is reversed?

A pendulum bob of mass m on a cord of length L is pulled sideways until the cord makes an angle [katex] \theta [/katex] with the vertical. The change in potential energy of the bob during the displacement is:

A simple pendulum consists of a sphere tied to the end of a string of negligible mass. The sphere is pulled back until the string is horizontal and then released from rest. Assume the gravitational potential energy is zero when the sphere is at its lowest point. What angle will the string make with the horizontal when the kinetic energy and the potential energy of the sphere-Earth system are equal?

Two masses m1 and 4m1 are on an incline. Both surfaces have the same coefficient of kinetic friction. Both objects start from rest, at the same height. Which mass has the largest speed at the bottom?

Ball A is dropped from a building of height H. Ball B is dropped from a building of height 3.5H. Using energy, what the ratio of vA to vB (final velocity of ball A to final velocity of ball B).

Two balls are dropped from the roof of a building. One ball has twice as massive as the other and air resistance is negligible. Just before hitting the ground, the more massive ball has ball ____ the kinetic energy of the less massive ball.

Find the escape speed from a planet of mass 6.89 x 1025 kg and radius 6.2 x 106 m.

A baseball is thrown vertically into the air with a velocity v, and reaches a maximum height h. At what height was the baseball moving with one-half its original velocity? Assume air resistance is negligible.

A car accelerates uniformly from rest to 29.4 m/s in 6.93 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate…