physics lab

PHYS 2011 - Lab 7: Work – Energy Theorem

Purpose: To test that the work done by gravity equals the change in kinetic energy of a falling object.

Theory: When an object of mass m falls through a distance d, gravity does work on it

equal to W=mgd. The work-energy theorem states that 2

2 12

2 1

if mvmvKW  . Thus, if one measures the final velocity of an object that is dropped from rest through a distance d, you can compare that with the final velocity predicted by the work-energy theorem.

If you measure the time it takes an object to drop from rest, the final velocity of the

object is gtgtgtvv if  0 .

Materials: Free fall Adapter, 2 steel balls (small ball m = 16 g, large ball m = 27.5 g ), 2- m stick

Procedure: 1. Set the drop apparatus so the height is just a bit above the height of the table. 2. Mount the small steel ball in the drop apparatus in the manner shown. It’s difficult

to explain in words. 3. Open software “Free Fall Adapter”. Double-click on “Digits” in the bottom left

pane, and choose “Time of Fall” from the list. 4. Test drop the ball and adjust the location of the strike pad until the ball strikes

near the middle. 5. Measure the distance the ball falls. Make sure to measure from the bottom of the

ball to the top of the strike pad. 6. Hit Start in DataStudio, drop the ball, and record the drop time in your log book.

Repeat four more times at the same height, for a total of five times. 7. Repeat steps 5 & 6 for the large steel ball – in other words, measure 5 drop times

at the same height for the large ball. Note that since the large ball has a different radius, you will have to re-measure the distance the ball falls

8. Change the height of the drop apparatus so that it’s near the top of the pole. 9. Mount the small steel ball again. 10. Measure the new distance the ball falls, as in step 5. 11. Measure 5 drop times for the small steel ball, record in your log book. 12. Switch to the large steel ball, re-measure the height of the ball, and measure 5

drop times for the large steel ball.

Analysis 1. Calculate the average drop time for each scenario. 2. Find the “measured” final velocity of the ball for each scenario using gtv f  . 3. Find the “calculated” final velocity of the ball for each scenario using the work-

energy theorem.

4. Compare the calculated final velocity to the measured final velocity (i.e. calculate a percent error) for each.

5. For each scenario, calculate the work done by gravity as the ball falls, and the change in kinetic energy. Compare the work done to the change in kinetic energy (i.e. calculate the percent error) for each scenario.

Questions 1. We neglected air friction in this lab. However, the difference between the work

done by gravity and the change in kinetic energy for each ball is almost entirely due to air friction. Estimate the work done by air friction for each scenario. For which ball does air friction generally play a larger role?

2. A 4.80 kg watermelon is dropped from rest from the roof of a 25.0 m tall building and feels no appreciable air resistance.

a. Calculate the work done by gravity on the watermelon during its displacement from the roof to the ground.

b. Just before it strikes the ground, calculate (i) the kinetic energy and (ii) the speed of the watermelon.

c. If we were to include air resistance, which of the answers in parts a) and b) would be different?