Investigating the speed at which a ball bounces off a surface

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Investigating the speed at which a ball bounces off a surface

Plan

Introduction

I intend on investigating the speed at which a ball rebounds of a given surface. I will try and find a relationship between the speed it hits the surface and the speed it comes off the surface.

Background Information

The principle of conservation of energy states “Energy cannot be created or destroyed, only converted from one form to another.”1 This is the reason that the ball does not rebound off the block at the same speed that it hits it at. As some of the energy has been converted into a different form when it hits the block.

Prediction

I predict that as the velocity of the ball approaching the surface increases then the speed at which it rebounds off it also increases proportionally. So if I double the speed of Va (velocity of approach) then the speed at which it rebounds is also doubled.

e.g.  Va    Vr. This means that the graph of my results should produce a straight-line graph as they are proportional (as shown in the diagram). This also means that the wooden block takes the same proportion of energy every time the ball hits the block

The reason why I think that the rebound speed will be slower than the approaching speed is that some of the kinetic energy from the moving ball is converted to the form of heat and sound when it hits the block. The kinetic energy of the ball has not been destroyed only changed its form, as quoted in my background information.

If an object of mass ‘m’ moves at speed ‘v’. Then we can say it has a kinetic energy of         ½ x m x v²

This means that the formula for the kinetic energy of the approaching ball is

K = ½ x m x Va² and so the formula for the rebounding ball must be K = ½ x m x Vr²

As I predict that they are both proportional to each other then I can form the equation ½ x m x Va²    ½ x m x Vr²

If I divide both sides by (½ x m) then I’m left with Va²    Vr² and by doing the square root of both sides then I’m left with Va    Vr. This shows that the relationship between them both must be proportional. In my experiment I intend on proving this relationship in the form of results.

        As the ball travels down the slope then some of the potential energy is gradually changed into kinetic energy, which causes the ball to gain momentum. Then as it hits the wooden block then this energy turns into elastic potential energy and some of the energy is lost in the form of sound and heat. As the ball bounces off the block the remaining energy is converted back into kinetic energy and it rolls back in the opposite direction. I will do two different methods and then compare the results collected from each of them. Then I will be able to see which method is more accurate in finding the speed of the ball and will also have something to compare my results against.

Key Variables

  • Velocity of approaching ball
  • Velocity of returning ball
  • Ball mass
  • Ball material
  • Surface material
  • Size of the ball

The variable that I have chosen to investigate is the velocity of the approaching ball. I can do this by changing the angle between the plastic ramp and the bench. By using the same ball for all my results this ensures that the ball material, size and mass remain the same. I will do the whole experiment on the same bench and use the same wooden block for the surface that the ball bounces off, so that the friction and surface material remains constant throughout. By only changing one of the variables and keeping the others constant this means that the experiment will be a fair test.

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Methods

You will need

  • A spherical wooden ball of diameter 2cm
  • A 45cm plastic V shaped ramp
  • 2 50cm rulers accurate to 1cm
  • A wooden block with a G-clamp
  • A stand and clamp
  • A light gate connected to a computer
  • A stop-clock
  • A hard work surface.

Set up the experiment as shown in the diagram. The plastic ramp is supported by the stand and clamp and can be used to change the speed of the ball. The wooden block is also clamped to the bench with a G clamp. The two rulers should be placed between ...

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