Physics Coursework Gravity Investigation

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Julian Gertner 4c                28) 06) 04

Planning:

Aim:

To investigate the efficiency of the bounce of a golf ball at different release heights.

Scientific knowledge:

        In this experiment, the golf ball used will have undergone several types of energy transfers from the time of release to the time it reaches its’ bounce height. From the moment the golf ball is lifted from the floor, it contains gravitational potential energy (G.P.E). Therefore, the golf ball must contain gravitational potential energy when held at a release height. The formula for gravitational potential energy is:

                        G.P.E = Mass × Gravity × Height

It is clear that the formula is made of three measurements, mass, gravity and height. The mass of the golf ball would have been kept constant throughout the experiment, simply by using the same ball. Gravity is equal to, 9.81ms-2 on earth. Therefore, gravity remained the same throughout the experiment. The final measurement in the formula, height, doesn’t remain the same as there were different release heights. With this in mind, if the value for mass and gravity remain the same but the height varies, then the gravitational potential energy must vary with the heights. If the release height increases, the gravitational potential energy increases. For example, if the release height of the golf ball doubled, the gravitational potential energy of the golf ball would also double. The release height is directly proportional to the gravitational potential energy.

        The first energy transfer the golf ball undergoes, relevant to the experiment, is from the gravitational potential energy at the release height, to kinetic energy (K.E), from the moment the ball is released. The formula for kinetic energy is:

                        K.E. =          ½ × Mass × Velocity2   

The measurement that will vary in this formula is the velocity of the ball. Therefore, as the velocity increases, so too does the kinetic energy. The higher the ball is released, the higher the velocity of the ball as it keeps accelerating until the ball reaches its’ terminal velocity. If the height is increased, the ball has more time to accelerate, thus increasing the velocity. Terminal velocity is when the ball won’t travel any faster and has the most kinetic energy it can acquire as the force pushing down on the ball, gravity, is equal to the force pushing the ball up, air resistance or upthrust. These two forces take a certain time to reach a stage where they are balanced, which varies with different balls. However, the golf ball will not reach terminal velocity in this experiment as the maximum height from which the golf ball was released, was 2m and this height is not sufficient for the golf ball to reach its’ terminal velocity. Therefore, the velocity of the golf ball would have increased as the height increased, in this experiment. From this, one can say, as the height is increased, the velocity is increased. Therefore, as the gravitational potential energy is increased, the kinetic energy is increased.

The second energy transfer is from the kinetic energy, in the air, to strain energy in the ball’s surface, when in contact with the floor. Heat and sound energy is lost during this second energy transfer when the ball hits the floor as the ball creates friction with the surface of the floor. When the ball is travelling through the air, heat is also lost as air resistance is constantly applied. The friction between the ball and air resistance, and the friction between the ball and the floor, causes heat to be created, which is lost in the atmosphere. The ball hitting the surface of the floor causes sound waves to be emitted into the atmosphere, thus sound energy is lost. The more kinetic energy the ball has the more sound and heat energy is lost as more friction is created and more sound waves are emitted. Strain is a type of potential energy and the more kinetic energy the ball has when it hits the floor, the more the ball will compress and the more strain energy the ball obtains. The ball hits the floor with a certain force from the kinetic energy it previously had, pushing the ball into the floor and the floor exerts an equal force on the ball pushing it up away from the floor. This causes the ball to compress, which is the strain energy it now acquires. The more gravitational potential energy the ball has, the more kinetic energy, the more the ball compresses and the more strain potential energy the ball has. The strain energy causes the ball to expand creating the ball to exert another force pushing off from the floor. The forces are now unbalanced and the ball thus ascends to its’ bounce height.

Once the strain energy causes the ball to bounce, the energy is transferred back to kinetic energy. When the ball reaches its’ bounce height the kinetic energy is converted to gravitational potential energy, the balls original energy form at the release height.

Therefore, the more gravitational potential energy, the more kinetic energy, the more strain energy, the more kinetic energy carrying the ball up and the higher the bounce height.          

         

Prediction:

The bounce heights will increase directly proportional to the increase of the release heights and the efficiency will remain the same.

Theory: 

My prediction is based on the scientific knowledge (above) that the higher the golf ball is released, the higher the ball will bounce, unless the ball reaches terminal velocity. This is because the higher the ball is released, the more gravitational potential energy the ball has because height is directly proportional to gravitational potential energy. Once the ball has this gravitational potential energy it is transferred several times. From gravitational potential, to kinetic, to strain, back to kinetic and back to gravitational potential. The more gravitational potential energy the ball has to start with, the more it will have at the end. Therefore, the higher the ball is released at the start, the higher the ball will bounce at the end. The efficiency will remain the same as efficiency is:

Output            ×        100        =        Bounce height                ×        100        

        Input                                          Release height        

If the bounce height is increasing directly proportional to the release height, then the efficiency should remain the same.  

Prediction graph:        

Further Prediction:

The bounce heights will increase as the release heights increase, although as the release heights get higher, the bounce heights will increase less and less. Therefore, the efficiency will gradually decrease as the release heights increase.

Further Prediction Theory:

        As explained earlier, the bounce heights will increase as the release heights increase because the greater the gravitational potential energy. However, as the release heights get higher, the ball travels for longer and gets closer and closer to reaching its’ terminal velocity. Although the ball doesn’t reach its’ terminal velocity, the air resistance acts on the ball for longer as the release heights are increased. The ball still accelerates as it falls, however as the release heights get higher, the air resistance has longer to act on the ball and the ball doesn’t accelerate as much as would be expected. If the release heights were in direct proportion to the bounce heights, then it wouldn’t accelerate as much as would be expected and the velocity isn’t as much. This means the kinetic energy the ball acquires when falling, isn’t as much too. Furthermore, the strain energy and kinetic energy the ball obtains when ascending isn’t as much, so the bounce height isn’t as high as would be expected. With this in mind, the trend of the bounce heights would begin to curve in the graph and the efficiency would gradually decrease. This is because the output is not as high as it should be in direct proportion to the release height.      

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Further Prediction Graph:

        

Preliminary Work:

Preliminary Method:

        

The same method was used for the preliminary work as was used below, in the main experiment. However, different types of balls were used, released at different heights and bounced on different surfaces, as seen in the table above. Furthermore, in order to obtain readings for the hot squash ball, the ball was simply rolled on a bench several times to generate some heat.

Justification:

        

To achieve the most accurate result possible, it is ...

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