In a simulation on Earth, an astronaut in his space suit climbs up a vertical ladder. On the Moon, the same astronaut makes the same climb. In which case does the gravitational potential energy of the astronaut change by a greater amount? Justify your answer.

A 7.80-g bullet moving at 600 m/s penetrates a tree trunk to a depth of 4.80 cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet.N(b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.

During a rockslide, a 620 kg rock slides from rest down a hillside that is 710 m along the slope and 240 m high. The coefficient of kinetic friction between the rock and the hill surface is 0.28. (a) If the gravitational potential energy U of the rock-Earth system is zero at the bottom of the hill, what is the value of U just before the slide? (b) How much energy is transferred to thermal energy during the slide? (c) What is the kinetic energy of the rock as it reaches the bottom of the hill? (d) What is its speed then?

In the figure, a frictionless roller coaster car of mass m = 992 kg tops the first hill with speed v0 = 16.7 m/s at height h = 40.7 m. How much work does the gravitational force do on the car from that point to (a) point A, (b) point B, and (c) point C? If the gravitational potential energy of the car-Earth system is taken to be zero at C, what is its value when the car is at (d) B and (e) A? I know the first one is 0 J.

A 0.27-kg stone is held 1.2 m above the top edge of a water well and then dropped into it. The well has a depth of 5.6 m.   (a) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone–Earth system before the stone is released? (b) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone–Earth system when it reaches the bottom of the well? (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?

A block of mass m is dropped onto a relaxed vertical spring with spring constant k (see the figure). The block becomes attached to the spring and compresses the spring a distance d before momentarily stopping. Assuming that friction is negligible, while the spring is being compressed, what work is done on the block by (a) the gravitational force on it? W = mg d (b) the spring force? W = 1 k d² 2 (c) What is the speed of the block just before it hits the spring? v = 2gd- k d² ✓ m | NOTE: State your answers in terms of the given variables and g.

"20 kg bear slides, from rest, 8 m down a Lodgepole Pine tree, moving with a speed of 5.6 m/s just before hitting the ground. What change occurs in the gravitational potential energy of the bear Earth system during the slide?"

1 Name: I I. A person's heart and head are 1.3 m and 1.8 m above the feet, repectively. Determine the potential energy of 0.5 kg of blood in the heart relative to (a) the feet, (b) the head. 1 I I I I I | I I I I I I

When you throw a ball into the air, it usually falls back down. If you throw it a little harder, it will take it longer to fall back down. You can throw it so hard that it never falls back down to Earth. This launch speed is called the escape velocity. When you are far from Earth, the potential energy of an object with mass m can no longer be written as PE = mgh. Instead, we must use the equation М-т PE = -G .. 1" M is the mass of the planet you launch from. m is the mass of the object being launched. r is the distance from the center of the planet to the object being launched. G is a universal constant called the gravitational constant (6.67-10-" ). kg-s Notice that the potential energy is 0 when you are infinitely far away from the planet, and negative as you get closer.

A 0.23-kg stone is held 1.5 m above the top edge a water well and then dropped into it. The well has a depth of 5.3 m. (a) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone-Earth system before the stone is released? J (b) Taking y = 0 at the top edge of the well, what is the gravitational potential energy of the stone-Earth system when it reaches the bottom of the well? J (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well? J