Determine the relationship between the range of the jump achieved by the ski jumper and the dropping height on the ramp.

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A-Level Physics Practical Investigation

Walid Aboudi

Ski Jumping

Introduction:

        As we all know ski jumping is a worldwide sport in which athletes skate down a slope ramp, gaining speed that throws them in the air that makes them land some distance away. The distance travelled at the time when the jumper leaves the ramp, until he reaches the ground is known as the jump range.

        This interesting and challenging sport has a lot of physics behind it. Kinetic energy, gravitational force, motion, speed, height, time, distance and the athlete’s ability to reduce air resistance to his or her body (aerodynamic) are all factors that determine the athlete’s performance.

        This experiment represents a ski jumping slope through which we will investigate how physics is related to it.

Aim:

        The aim of my investigation is to determine the relationship between the range of the jump achieved by the ski jumper and the dropping height on the ramp. We will model the jumper as a ball and the ski slope as a bent plastic ramp.

Currently at this level we will not take air resistance, friction and other various type of energy lost into account.  However in practical we have to take in mind that they do exist and cause variation in our results.

Background knowledge and Predictions:

        I have decided to investigate how the vertical height of drop on the slope relates to the range achieved. One of the things a person can think of firstly is that the greater the height on the ramp, the greater the range will be. This is because more GPE is converted into KE.

        GPE stands for “Gravitational Potential Energy” and it is the energy that an object has at a certain height. The equation for it is:

 

GPE = mgh”, where “m” is the mass in Kg, “g” is the acceleration due to gravity in ms-2, and “h” is the height of drop in m.

        KE stands for “Kinetic Energy” and it is the energy of a moving object. The equation for it is:

   

KE = ½mv2, where “m” is the mass in Kg, “v” is the velocity in ms-1.

When the ball is at any point up the ramp, it would definitely have GPE, when the ball is released from rest, this will cause it to travel down the ramp, and this movement is KE. While the ball is travelling down the ramp, we can assume by neglecting air resistance and friction, or any other form of resistance causing energy being wasted, that GPE is converted to KE, therefore we can equate the two equations to each other:

GPE = KE

=> mgh = ½mv2

Since the two masses will cancel out while acceleration due to gravity is assumed to be remaining constant, we can say that as height increases, the velocity gain would increase proportionally.

        In order to calculate the range, we have to find the horizontal and vertical component separately. Since we are ignoring any type of resistance, the ball which is modelled as a particle should have a constant horizontal velocity at the moment it reaches the end point of the ramp, in other words, when it is parallel with the table.

gh = ½v2

Note: Also at that point all the GPE would have already changed to KE.

Since it is parallel to the table, therefore h=0, and if h=0 then “v=0

At the moment it leaves the ramp it will move freely under gravity causing only a downward acceleration. As a result the drop height has no effect on the horizontal velocity but vertically. Hence this is the component which determines the time of flight.

 

Vertical Component                                        Horizontal component

By equating the vertical components,                By equating the vertical components,  

                                                                           

GPE lost = KE gained                                      

      mgh  =  ½mv2 

         gh  =  ½v2

           v  = √(2gh)

 

Now finally after we found the velocity and the time, it would be very easy to calculate the range using the velocity equal distance divided by time equation, which is equal to:-

Range = Velocity * Time

r = [√ (2gh)] * [√ (2s/g)]

                                                        r = 2 √hs        

Using this theoretically equation, we can replace the height of drop “h” and by the drop height “S”, and that should give us the range “r”.

Join now!

After thorough research on the internet and books, I found that a moving ball has both linear and rotational kinetic energy. This new kind of energy is called Rotational Kinetic Energy or RKE. To make a body which is initially at rest start rotating about a fixed axis, it is necessary to apply a torque to the body. The torque does work on the body and in the absence of friction; the work done increases the KE of the body. Therefore the body rotates faster and faster. The kinetic energy of a rotating body is given by:

RKE ...

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