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# Investigation into the range of a ski jump

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Introduction

## 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.

Middle

R (√R²)

5

85

340

1700

41.2

10

85

340

3400

58.3

15

85

340

5100

71.4

20

85

340

6800

82.5

25

85

340

8500

92.2

30

85

340

10200

101

35

85

340

11900

109.01

40

85

340

13600

116.6

45

85

340

15300

123.7

A graph of h1 against R² will be plotted using the above-predicted results alongside my actual results. This will enable me a direct comparison between the two.

Time plan:

- One hour will be spent performing the experiment.

- It will take 20mins to setup all the apparatus

- 30mins to take results, including disaster time (in case things go wrong)

- 10mins to pack away apparatus

Ranges:

A range of h1, from 5cm to 45cm will be recorded in 5cm intervals.

The range will be recorded from approximately 0cm-150cm

H2 will be measured before beginning the experiment, as it is a constant.

Reliability:

Unreliable results are caused by random error. When a single recording is made the result may not be the true result, it may be close, but due to experimental circumstances (for example the ball is blown slightly off course) there is an error in that particular result. Therefore repetitions of the experiment will allow these errors to be spread evenly around the correct value. Giving a true impression of the answer.  Few results are recorded giving a false impression of the correlation. Many results are recorded giving the true result.

Sensitivity:

This concerns the accuracy of the equipment. In this experiment say, for example, that a microscope is used to read the values from the ruler accurately. The low power microscope allows the scientist to distinguish to an accuracy of ±0.1mm, but the ruler markings are only accurate themselves to ±1mm. This means that a compound error is formed and shows why appropriate measuring methods should be used in conjunction with measuring equipment.

In this case an attempt to improve accuracy only serves to waste time and equipment. Appropriate equipment must be applied in each situation.

Accuracy:

Conclusion

Therefore if the ramp is uneven and the ball doesn’t travel down the middle of the ramp, range will be lost, producing less accurate results.

In future experiments it would be sensible to use a combination of a spirit level and careful measuring to ensure the ball travels straight down the ramp. A more restricting track would be another option, it would mean the ball follows a set path.

Another factor affecting the speed of the ball is the way in which it travels down the ramp. It could slide or skid instead of rolling meaning that the ball is not gaining rotational kinetic energy and losing its potential energy as it should. Instead it is falling, resulting in an incomplete energy transfer, so the ball doesn’t reach maximum speed when leaving the ramp. This effect may be reduced using a ramp with a more gripping surface.

Even the smallest factors can contribute to an overall large effect. Sound energy caused by friction between the ramp and ball can reduce the amount of energy the ball has as it leaves the ramp. Sound energy is a factor that cannot be removed easily, unless working in a vacuum where sound waves cannot travel. But it is such a small factor that it is unlikely that it would affect the results in any considerable way.

Next time:

If this investigation were to be repeated, a different approach would be adopted. More care would be taken to ensure that the above factors were minimised. Many more results would be taken to provide a more reliable end result and fairness would be looked into seriously.

A light gate setup could be used to check the speeds at which the ball leaves the ramp, this result could then be considered with the mass and used to calculate the kinetic energy (KE=½mv²). The gravitational potential energy could also be calculated (GPE=mgΔh1) and the energy loss calculated.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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