Question

Part 1: Ball Toss: Conservation of energy, or not, as a ball travels through the air

Open BallToss.cmbl with LoggerPro. Find the height and velocity of the ball at three points: initial, right after it left the hands, peak, and final, right before it was caught. Compute the potential energy, kinetic energy, and PE + KE of the ball at these three points.  Use whatever reference point seems convenient -- the location of the detector is fine.

   

Mass of ball: 621.2 g ± 0.2 g, or  621.2 g ± 0.03%         g: 9.8 m/s² ± 0.03%

	Height of ball	Velocity of ball	PE of ball	KE of ball	PE+KE of ball
Initial
Peak
Final

          ± 1 mm                  ± 1%                 ± 0.4%           ± 2%            ± 0.06 J

Conclusion: Was the ball’s energy conserved as it travelled through the air?  Explain.

(A good explanation includes % errors and compares them to expected uncertainty, and discusses the causes of errors if the answer was not as expected.)

Part 2: Ball Drop: Loss of energy in each collision with the floor

  Open BallDrop2.cmbl with LoggerPro. Find the height of the floor (height of the top of the ball when the ball touches the floor), the initial height of the ball (relative to floor) right after Prof. Schnal dropped it, and the peak height (relative to floor) at the top of each of the first three bounces. Note that the detector was not reversed so the graph is upside down, as if “up” were positive. Compute the initial potential energy, the potential and kinetic energy at the top of each bounce, the total mechanical energy at the top of each bounce, and the % energy lost in each collision with the floor.

Distance from LoggerPro to floor (use the data point where ball is farthest from detector):

	Distance to detector	Height above floor	Velocity at peak	PEpeak	KEpeak	PE+KE at peak
Initial (right after it leaves your hands)							% energy lost in collision
Peak of 1st bounce
Peak of 2nd bounce
Peak of 3rd bounce

      ± 1 mm        ± 1 mm                             ± 0.5%    ±2%      ±2.5%   

Part 3: Ball rolling down ramp: Loss of energy due to (you figure out what)

  In the projectile motion lab, a ball was placed at the top of a ramp. In one case, its initial height was 12.0 cm above the table top, and it rolled off the table with velocity v =  1.12 m/s.  Compute the initial potential energy relative to the height of the table top, final kinetic energy as it leaves the table top, and % energy lost.  

Mass of ball: 100 g ± 50 g  (We did not measure its mass. Mass divides out and doesn’t affect calculation of % energy lost.)

	Height of ball	Velocity of ball	PE of ball	KE of ball	PE+KE of ball
Initial (top of the ramp)
Final (as it passes through  the photogates)

% energy lost:

Conclusions: Think about how the ball moved down the ramp and across the table, and explain where the missing energy went.  I can think of three specific mechanisms that would have transferred significant energy from the ball to the environment. You might need to try it again at home to see: roll a hard ball down a rigid homemade ramp and across a table top.  

Extra Credit, up to 5%:  Upload a picture of your homemade ramp setup.  You can see a couple of things happening as it goes down the ramp and across the table that take energy from the ball.  You may have extra credit if you both upload a picture and correctly identify at least two things happening that would dissipate energy.

Answer 1

We have,
Initial height of the ball
Initial velocity of the ball
Mass of the ball
Gravitational acceleration

At the height the initial velocity of the ball is just after leaving the ball from the top of the ramp.

Initial potential energy of the ball at height just after leaving the ball is calculated as:

Initial kinetic energy of the ball just after leaving the ball is calculated as:

Total initial energy of the ball just after leaving the ball is calculated as:

Final height of the ball is at the end of the ramp. The final velocity of the ball just before coming to rest is calculated from the kinematics formula:

  

Final potential energy of the ball just before coming to rest is calculated as:

Final kinetic energy of the ball just before coming to rest is calculated as:

Total final energy of the ball is just before coming to rest calculated as:

Energy lost in the ball is calculated as:

This energy loss is conversion of total energy into thermal energy due to friction of the ball with ramp surface. Since frictional forces are non-conservative, thermal energy cannot be taken into work.

The percentage difference between the initial total energy and final energy of the ball gives percentage energy loss: