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Investigating an aspect of physics that is relevant to ski jumping.

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Mufadal Jiwaji        PGM        02-May-07

Investigating an aspect of physics that is relevant to ski jumping image00.png

Aim:        To investigate the effect of varying the perpendicular height of a ramp on the distance travelled by a marble, which has descended the ramp and has been projected in a horizontal direction.

Prediction of the relationship between the height used and the change horizontal distance travelled by the spherical mass.

I believe that height is directly proportional to distance squared. This means that if the height is doubled the distance will quadruple.

Explanation of the prediction in scientific terms.

The formula to work out distance travelled is simply = average speed/total time, however there are many other formula used in working these two out. First the speed, or velocity must be obtained. The velocity of the ball does not depend on the length of the ramp (if friction is discounted) but on the vertical height the ramp is set at or ‘h’. Using previously obtained scientific knowledge I understand that GPE (gravitational potential energy) = kinetic energy. Therefore mgh (mass × gravity × height of ramp)=0.5mv2(0.5 × mass ×velocity squared). Due to there being mass on both sides of the equation it is mathematically acceptable to divide the mass out so the formula looks like so: gh = 0.5v2.

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ime                 =                 √2s / aimage03.png

It is now possible, knowing just the height of the ramp, the height that the ball will fall and gravity to work out how far the ball will travel. Distance = average speed × total time taken. To determine the average speed we take the final velocity and divide it by 2 therefore:

Distance         =         0.5V × t

However, this does not fully explain why the height is directly proportional to the distance squared. The time taken for the ball to drop is always constant, the distance the ball is dropping will remain the same throughout and so will the acceleration (9.8ms-2), therefore we can disregard the time in dealing with the relationship. When working out the velocity the 2g is always the same, therefore that can be disregarded. Therefore the only variable is the square root of the height and so using mathematical deduction the distance must be directly proportional to the square root of the height. This can be rearranged as follows:

Distance2         α                 Height

Brief account, including any data obtained, of the preliminary practical work carried out.

The preliminary work was used to provide good understanding in the practical and help us decide important parts of out method. Many apparatus set-ups were experimented with, ranging from the completely unfeasible to some that provided a large part of the final method.

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Explain clearly how your results would be processed and what your expectations are.

From the above method an accurate set of results ought to be produced and there are many things that can be done to these statistics that may be helpful. I suggest a scatter graph of height (on the x axis) against distance squared. I expect there to be a smooth gentle curve upwards, with possibly an anomaly on the way. An example graph that I have constructed is on the next page, this is how I believe my plan will lead to my results being like.

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