Question

A 0.513-kg basketball is dropped out of a window that is 5.29 m above the ground....

A 0.513-kg basketball is dropped out of a window that is 5.29 m above the ground. The ball is caught by a person whose hands are 2.06 m above the ground. (a) How much work is done on the ball by its weight? What is the gravitational potential energy of the basketball, relative to the ground, when it is (b) released and (c) caught? (d) What is the change (PEf - PE0) in the ball's gravitational potential energy?

Homework Answers

Answer #1

The work done on the ball by the force of gravity as it travels from the window (a distance h0 above the ground) to your friend's hands (a distance hf above the ground) may be determined by
W = Fg(h0 − hf) cos 0°
= mg(h0 − hf)
= (0.513 kg)(9.80 m/s2)(5.29m − 2.06 m)
= 16.24 J.

(b) The potential energy of the ball-Earth system relative to the ground when released is:
U0 = mgh0
= (0.513 kg)(9.80 m/s2)(5.29m)
= 26.595 J.

(c) The potential energy of the ball-Earth system relative to the ground when caught is:
Uf = mghf
= (0.513 kg)(9.80 m/s2)(2.06 m)
=10.35 J.

(d) Since the force of gravity is a conservative force, the work done on the ball by the force of gravity is the negative of the change in gravitational potential energy of the ball-Earth system. This may be expressed as:
W = −ΔU
which leads to the ratio
ΔU /W = −1.
In other words: (Uf - U0)/W = (10.356-26.595)/16.24 = -1

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
While leaning out a window that is 5.7 m above the ground, you drop a 0.60...
While leaning out a window that is 5.7 m above the ground, you drop a 0.60 kg basketball to a friend at ground level. Your friend catches the ball at a height of 1.2 m above the ground. Determine the following. (a) the amount of work done (in J) by the force of gravity on the ball J (b) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released J (c) the...
While leaning out a window that is 6.1 m above the ground, you drop a 0.60...
While leaning out a window that is 6.1 m above the ground, you drop a 0.60 kg basketball to a friend at ground level. Your friend catches the ball at a height of 1.3 m above the ground. Determine the following. (a) the amount of work done (in J) by the force of gravity on the ball ( ) J (b) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released (...
Part 1 While leaning out a window that is 6.5 m above the ground, you drop...
Part 1 While leaning out a window that is 6.5 m above the ground, you drop a 0.60 kg basketball to a friend at ground level. Your friend catches the ball at a height of 1.2 m above the ground. Determine the following. (a) the amount of work done (in J) by the force of gravity on the ball ___________ J (b) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released...
A ball is thrown vertically upward from a window that is 3.6 m above the ground....
A ball is thrown vertically upward from a window that is 3.6 m above the ground. The ball's initial speed is 2.8 m/s and the acceleration due to gravity is 9.8 m/s^2. a) What is the ball's speed when it hits the ground? b) How long after the first ball is thrown should a second ball be simply dropped from the same window so that both balls hit the ground at the same time?
A ball of mass 2.25 kg is released from rest at height 5.29 m above the...
A ball of mass 2.25 kg is released from rest at height 5.29 m above the floor. It falls, hits the ground, and rebounds to height 3.19 m above the floor. Assume none of the losses are due to air friction. Find the impulse, in N-s, exerted by the floor on the ball. The sign of your answer will give the direction of the impulse.
A 1.5 kg ball is dropped from a height of 3 m above the ground and...
A 1.5 kg ball is dropped from a height of 3 m above the ground and upon striking the ground bounces up to a height of 2 m. Ignoring air resistance, find the time it takes the ball to bounce up to a height of 2 m after it is dropped.
A 57.8-kg skateboarder starts out with a speed of 1.98 m/s. He does 82.3 J of...
A 57.8-kg skateboarder starts out with a speed of 1.98 m/s. He does 82.3 J of work on himself by pushing with his feet against the ground. In addition, friction does -232 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 8.47 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give...
A 51.8-kg skateboarder starts out with a speed of 2.28 m/s. He does 105 J of...
A 51.8-kg skateboarder starts out with a speed of 2.28 m/s. He does 105 J of work on himself by pushing with his feet against the ground. In addition, friction does -251 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 6.36 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give...
A 61.5-kg skateboarder starts out with a speed of 1.71 m/s. He does 105 J of...
A 61.5-kg skateboarder starts out with a speed of 1.71 m/s. He does 105 J of work on himself by pushing with his feet against the ground. In addition, friction does -298 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 5.93 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give...
A 63.3-kg skateboarder starts out with a speed of 1.67 m/s. He does 81.1 J of...
A 63.3-kg skateboarder starts out with a speed of 1.67 m/s. He does 81.1 J of work on himself by pushing with his feet against the ground. In addition, friction does -280 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 6.37 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give...