Investigation into the range of a ski jump

Authors Avatar

Investigation into the range of a ski jump

Introduction:

The task is to investigate into the range of a ski jump based upon two variables, h1 and h2. Using knowledge of projectile motion investigate how the ramp height and drop height affect the range of a marble released from the ramp.

This is a diagram of the basic equipment setup.

First thoughts:

This investigation has much room for expansion on the original above setup. The accuracy can be improved using a combination of more sensitive measuring equipment and a more accurate measuring setup.  A formula linking h1, h2 and the range will be produced and will be linked to the graph that will be plotted alongside the practical experiment.

Derivation:

Velocity = displacement

                 time

Displacement = velocity x time

This equation allows the calculation of the range, so velocity and time must now be found.

m=mass, kg

g=9.81ms-²

h1=height1, m

h2=height2, m

v=velocity, ms-¹

s=displacement (the range), m

u=initial velocity, ms-¹

t=time, s

a=acceleration (also g in this case), ms-²

Velocity:

Assuming no energy is lost, potential energy is equal to kinetic energy.

PE=KE                                (PE or GPE= mgΔh1)

mgΔh1=½mv²                        (KE=½mv²)

mgΔh1mv²                        Masses cancel

½v²=gΔh1                        x2, √

v=√(2h1g)

Time:

Using s=ut+½at² and looking in the vertical direction.

s=ut+½at²        

s=0+½at²                        0 vertical velocity

h2=½at²                        a=g

h2=½gt²                        x2, √

t=√(2h2 /g)

Now the two equations can be combined to produce one equation, in the form:

displacement = velocity x time

R=√(2h1g) x √(2h2 /g)                g cancels

R=√(2h1) x √(2h2)

R=√(4h1 h2)

Experimental setup:

1)

A diagram of the chosen apparatus set-up

2)

A diagram detailing the release mechanism and method of recording

3)

A diagram detailing the method of recording

Plan:

  1. Before the experiment is setup, all equipment is tested. Particular factors to be tested are the straightness of the ramp (covered in accuracy later on) and the sensitivity of the carbon paper.
  2. Next, apparatus is setup as in diagram 1.
  3. Fastenings and stability of the apparatus are looked at. G clamps are checked as well as the boss, clamp and stand construction.
  4. Approximate range determination: using setsquare placed next to the first height, ball position is determined. Ball is aligned manually and then dropped (diagram 2).
  5. Ball falls and then approximate landing position is taken note of.
  6. Carbon paper is then positioned in the approximate landing zone.
  7. Using the setsquare placed at the first height, ball position is determined. Electromagnet is lowered into position and then switched on. Ball is magnetised and then electromagnet is moved again, so that the bottom of the ball is at the desired height (as in diagram 2).
  8. Electromagnet switched off, ball is demagnetised and rolls down the ramp and off the edge of the table, landing on the carbon paper.
  9. The distance from the edge of the table to the mark on the carbon paper is measured and then recorded (as in diagram 3).
  10. This process is then continued until all results have been taken.

Data interpretation:

Alongside doing the experiment a graph should be plotted. This will allow any correlations to be spotted early on and then further predictions to be made. It will also allow the scientist to investigate anomalies.

For example:

The graph is being plotted as the experiment is taking place. An odd result is spotted (circled).

Join now!

Further points can then be recorded around the odd result. A new trend can now be noticed. Without plotting the extra points, the result would just have been taken as an anomaly. Therefore drawing a graph alongside the experiment place allows for greater scientific accuracy and better end results.

Graph:

In this experiment a graph of R against h1 would seem suitable at first thought.

The previously derived formula:

R=√(4x h1 x h2)

When used in a graph this formula would not give any sort of relevant ...

This is a preview of the whole essay