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# Examine the relationship between the height a ball is dropped from and the vertical distance from the point of impact that its first bounce travels.

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Introduction

Investigation to find out what affects the height that a golf ball bounces to

Aim: I wish to examine the relationship between the height a ball is dropped from and the vertical distance from the point of impact that its first bounce travels.

Apparatus: Tape Measure, A Golf Ball, Ping Pong Ball, Floor

Plan:

Using a tape measure suspended and weighted at the bottom (to ensure verticality), measure the appropriate starting height. The centre of the ball should be aligned with the relevant markings on the tape and dropped so that the tape does not foul the path of the ball. A spotter should be ready to sight up the height of the bounce and as level with the apex of the balls path as possible. A tolerance of 10mm is realistic. This should be repeated five times each at heights of 0.5m, 1m, 1.5m, 2m and 2.5 meters.

In this experiment I will measure the height reached after the bounce, because that is what I wish to investigate. I will also need to measure the independent variable, the height at which the ball is dropped from. To measure both of these I will use metre sticks and I think that they will be accurate enough considering that we will only have someone’s judgement to go by with regards to how high it bounces to.

Middle

Momentum: The formula for momentum is Momentum = Mass × Velocity. It is possible to work out the average velocity of the falling ball using the formula v=√ (2gh)(a rearranged version of the formulas for gravitational potential energy and kinetic energy). Since the only thing within this formula that will change is the height it is possible to see that a ball dropped from a higher height will have a higher average velocity, unless it reaches terminal velocity. Therefore a ball dropped from a higher height, having a bigger velocity will subsequently have more momentum. Before colliding with the floor the momentum of the ball is its mass multiplied by its velocity and the momentum of the floor is 0. When the ball hits the floor it stops momentarily but because of the conservation of momentum the momentum must still exist after the collision in the particles of the floor and the ball, which are now moving. When the ball bounces up again the particles are still moving so they have some momentum which means that the ball cannot have as much momentum as it did before the collision and therefore, since its mass has not changed it must have a smaller velocity.

Elasticity: Elasticity is the ability of a solid to recover its shape once deforming forces are removed. A golf ball has this ability due to the elastic bands inside it.

Conclusion

Despite all the inaccuracies in the method the results seem surprisingly accurate. The averages fall in a near perfect straight line, which would suggest that they are accurate. Assuming the results were read fairly accurately it would lead me to believe that the other issues of inaccuracy are fairly negligible. To achieve such a straight line probably means that our results are accurate enough to base a conclusion on.

The experiment could be made more accurate by filming each bounce and playing it back in slow motion to obtain more accurate measurement, for example to the nearest 5mm. I could also go to extra lengths to make sure that the ball landed in exactly the same place each time and that it was dropped and not thrown.

The results are fairly reliable because we repeated each height five times so that anomalous results would become obvious. Very few of our results varied that much within each height and therefore our results are probably quite reliable. In order to make the results even more reliable more repeats could be carried out, however I do not think this is entirely necessary as the heights reached were always so close to the same percentage.

If I were to complete a similar experiment I would wish to find out if after a certain height the golf ball can no longer maintain the percentage height reached after a bounce, as I discovered with the ping-pong ball. I would also like to see if the same percentage of height is lost after a second, third, fourth or fifth bounce etc.

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