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

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        NOTTINGHAM HIGH SCHOOL

Mufadal Jiwaji        PGM        02-May-07

Investigating an aspect of physics that is relevant to ski jumping

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. Using simple mathematical techniques we can rearrange that formula to provide us with the following equation which gives us the final velocity:

                   

     Velocity        =  √  

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Now it is possible to work out the final velocity of the ball as it hits the bottom of the ramp using this equation.

The second half of the formula to work out distance requires the time taken. Using required knowledge I know that it takes a same amount of time for a ball to drop from a certain height vertically, that it would if it was travelling with velocity horizontally. To work out the time taken, for a ball to drop vertically downwards, one of the UVAST equations needs to be used. In particular the ...

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