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# Investigatin a ski jump

Extracts from this document...

Introduction

Scott Jenkins

Investigating a ski-jump

Aim:To investigate how the starting position of a ski jumper affects the horizontal distance travelled in the jump. I will not take air resistance, friction and other various type of energy lost into account, however in practical I have to keep in mind that they do exist and cause variation in my results.

Introduction

Ski jumping is a sport event that involves a steep ramp and a landing zone, where the skier has to travel as far as possible after leaving the ramp horizontally. When the skier is in motion in the air and the range it reaches is what I am investigating. This motion is called the projectile motion and the displacement, velocity and acceleration of the projectile are all vector quantities. Each of these can be placed into vertical and horizontal components. In my experiment, I will create a similar model of the ski jump using a plastic curtain rail as the slope and model the skier as a particle, in this case, a ball bearing.

Diagram                                    This is a diagram of the basic equipment setup

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.

Background Knowledge

Speed = Distance                                        Re-arrange

Time

Range = Velocity x Time

X= VT……….Equation 1

To find the range (x), the velocity and time must be found.

m=mass, kg
h=height1, m
H=height2, m
v=velocity, ms
-¹
s=displacement (the range), m
u=initial velocity, ms
-¹
t=time, s
a=g=9.8, ms
-²

Middle

The distance from the edge of the table to the mark made in the sand is measured and then recoded.This is process is then repeated untill all results have been collected.

Safety Precautions

There are few minor risks in doing this experiment, which with careful setting up and appropriate behaviour, can be avoided. These are:

• When bending down to record measurements of the range, it is possible to bas your head coming up. Simply be aware of your surroundings.
• Having a sand pit on the floor can prove to be an obstruction to passers-by and can be a hazard of tripping over. I will make sure there are no obstructions by the landing zone when in practise.
• The ball bearing is heavy enough to cause injury to anyone if hit by it. Keeping distance should prevent this.

Data interpretation

Alongside doing the experiment I will plot a graph. This will allow for any correlations to be spotted early on and then further predictions to be made. It will also allow the investigattion of anomalies. Therefore drawing a graph alongside the experiment allows for greater scientific accuracy and better end results.

Sensitivity

The sensitivity of this experiment is concerned with by the accuracy of the equipment available. For example, a much more accurate measuring device can be used to distinguish to an accuracy of ±0.1mm, but the ruler markings are only accurate themselves to ±1mm. Therefore, this creates a small error and show that to get the best out of the results, the most accurate equipment should be used in all situations.

Accuracy

Conclusion

Ie. At a height of 5cm, the mean result was 31.33cm. However this can actually be smaller or bigger than this value considering the errors in apparatus. The position of the plumbline to mark the the edge of the table will have an estimated ±2mm, having to join 2 meter rulers together will have an estimated ±1mm and judging the landing position of the ball will also have a ±2mm effect on the results. In total the range of values for the results will be ±5mm. Therefor the range of values for 31.33cm would be 30.83cm – 31.83cm.

Percentage error

I will take the maximum result of the range and calculate the percentage error based on the uncertainty values.

% error of range, x, 93.33cm ± 0.5cm

0.5cm ÷ 93.33cm x 100% = 0.53%

The values are vastly small and so are not worth considering.

Improvements

If this investigation were to be repeated, there are a few things I would like to change.

Firstly, I would ensure to take more care that the above factors were fully compramised and minimised.

Furthermore, I would take a much larger range of results to provide a more reliable end result, taking fairness of the experiment into account much more seriously.

Finally, I would use a much more accurate range of apparatus to get the most accuracy in my results. For example, a specialised light gate can be set up at the end of the ramp to dictate the exact speed at which the ball leaves the ramp. This could then be considered with the mass to calculate the kinetic energy and gravitational potential energy and hence the total energy loss.

Bibliography

• Various web pages for research

This student written piece of work is one of many that can be found in our AS and A Level Mechanics & Radioactivity section.

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Equation 3 Equations 2 and 3 can now be substituted into equation 1. Range(x)=Velocity(v) x Time(t) R=V(2gh) x V(2H /g) g cancels out R=V(2h) x V(2H) R=V(4hH)............ Equation 4 Assumptions 1. The friction between the ball and the curtain rail, along with the air resistance are neglible, therefore, will not be accounted for in this experiment.

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