Bouncing Ball

Name : Adam Okoe Mould Title : Bouncing Ball Criteria : Dn, DCP, CE Research Question : What is the relationship between the height at which a tennis ball is dropped and its maximum rebound height? Hypothesis : For small heights, the drop height will be proportional to the bounce height because when the drop height is reduced, the ball hits the ground with less force and therefore the rebounded force will be less and the ball would rebound to a lower rebound height. Apparatus • • • • •

Tape Measure Tennis Ball Ruler Flat Horizontal Surface Vertical Section of Wall

Variables Independent Variable •

Drop Height – The initial height the tennis ball drops

Dependant Variables •

Rebound height – Maximum height of first bounce

Controlled Variables •

•

Surface on which the ball bounces – This is because different balls have different degrees of hardness and therefore different hardness of floors will cause different absorption of energy when the ball hits the ground causing varying rebound heights for the same drop height. Tennis Ball – The same tennis ball would be used because the mass will affect the acceleration of the ball and also different balls absorb energy to different extents on impact.

Procedure 1. Cellotape a tape measure against a vertical wall with measurements ranging from 0 cm to 200cm. 2. Let one experimenter hold the tennis ball with the fingers and place the top of the ball in line with the 200cm mark of the tape measure. 3. The second experimenter should be positioned near to the floor. 4. The first experimenter should drop the ball from the 200cm mark whiles the other experimenter observes the height of the bounce (this is a trial drop since the second experimenter needs to know the approximate height of the bounce since he has to be level with the measuring scale to avoid parallax error.) 5. This observed height should be marked with a ruler by the second experimenter. 6. To ensure accuracy, the same drop is repeated before the rebound height is recorded. 7. Repeat these steps twice for drop height increasing and drop height reducing for about 10 different drop heights. 8. Find the average for the rebound heights Precautions 1. Ensure that the surface of the floor is horizontal because on trial runs it was observed that when the ball landed on a slanted surface the ball rebound with a horizontal and upward motion instead of a perpendicular upward motion. Raw Data Drop height /cm± 0.05cm 200.00 192.00 180.00 160.00 153.00 140.00 120.00 112.00 81.00 76.00

Rebound Height /cm ± 0.05cm Drop Height Drop Height Increasing Reducing 108.00 107.00 103.50 104.00 99.00 100.00 87.00 87.00 84.00 84.50 76.00 75.50 68.00 69.00 59.00 56.00 46.00 45.00 43.50 44.50

Observations As the drop height reduced, the rebound height also reduced. Also the loudness of the sound heard when the ball hit the ground reduced as the drop height reduced.

Processed Data Rebound Height / m ± 0.0005m Drop Height / m ± 0.0005m

Run 1 , Drop Height Increasing

Run 2, Drop Height Reducing

2.0000 1.9200 1.8000 1.6000 1.5300 1.4000 1.2000 1.1200 0.8100 0.7600

1.0800 1.0350 0.9900 0.8700 0.8400 0.7600 0.6800 0.5900 0.4600 0.4350

1.0700 1.0400 1.0000 0.8700 0.8450 0.7550 0.6900 0.5600 0.4500 0.4450

Average Rebound Height /m ± 0.0005m 1.0750 1.0375 0.9950 0.8700 0.8425 0.7575 0.6850 0.5750 0.4550 0.4400

Calculations Drop Height in meters = Dropt Height in cm × 100 ∆ Drop Height in meters = ∆Dropt Height in cm × 100 = 0.05cm × 100 = ± 0.0005 m Rebound Height in meters = Rebound Height in cm × 100 = 0.05cm × 100 = ± 0.0005 m Average Rebound Height = (Rebound Height run 1 + Rebound Height run 2) ÷ 2 ∆Average Rebound Height = (∆Rebound Height run 1 + ∆Rebound Height run 2) ÷ 2 = (0.0005 + 0.0005) ÷ 2 = ± 0.0005m

Graph of Rebound Height against Drop Height

2

y

1.8 1.6 1.4 1.2 1 0.8 0.6

rs ight/m eboundH R

0.4 0.2 x -0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1

Drop Height / meters

Comments on Graph • There were enough data points plotted since it was able to eliminate enough random errors like the first and third coordinates. • The coordinates were fairly precise as they were scattered above and below the line of best fit • The uncertainty bars are negligible as they can not be seen from the graph • The intercept was a negligible difference of 0.002 units from the origin. • The graph of rebound height against drop height shows that the rebound height is directly proportional to the drop height because the line of best fit was a straight line passing through the origin.

Conclusion The drop height of a tennis ball is directly proportional to its rebound height as the line of best fit was a straight line passing through the origin for the graph of rebound height against drop height. As many drop heights were taken, the experiment was successful despite a few random errors. Sources of Error 1. Due to the limitation of the human eye, it was difficult to observe the measured mark of the rebound height as it remained at its rebound height only momentarily. 2. It was noticed that most of the random errors occurred when the drop height was low. This may have been because the experimenter could not bend low enough to be level with the ball. Hence, parallax error may have caused these random errors. Improvements to the investigation 1. A camera with a high number of megapixels with the appropriate software can be used to accurately determine the rebound height. 2. To reduce random errors caused by parallax error, use drop heights above 120 cm so that the experimenter would not have any difficulty in bending low to be level with the tennis ball