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An investigation to find out how gravitational potential energy is converted into kinetic energy.

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Introduction

An investigation to find out how gravitational potential energy is converted into kinetic energy.

I will be investigating, how gravitational potential energy is converted into kinetic energy. My experiment will involve a trolley, after being released from rest, rolling down a ramp.

(The following abbreviations will be used in this document:

k.e.: Kinetic energy, p.e.: Potential energy.)

At the top of the ramp the trolley has gravitational potential energy, once it is released this energy is converted to kinetic energy when the trolley is moving.

The following theoretical knowledge has been adapted from “Advanced physics” by Tom Duncan.Gravitational potential energy is the energy stored in an object as a result of its vertical position (i.e., height.) The energy is stored as the result of the gravitational attraction of the earth on the object. There is a direct relationship between the potential energy, the mass of the object and also the height of the object. The formula for Gravitational potential energy is:

G.P.E = m × g × h     ( mass (kg) x gravitational field (m.s-2)x height(m) )

In my case I am using the same trolley so the mass is the same, but I am changing the height of the ramp; the higher the trolley is elevated the greater the potential energy is. The gravitational field strength will remain constant.

Kinetic energy is the energy of a body resulting from motion. Kinetic energy depends upon two variables: the mass (m) of the object and the speed (v) of the object. The formula for Kinetic energy is

K.E=½ × m × v2         (½ × mass (kg) ×velocity (m.s-1)  squared)

Middle

Method

Set-up the equipment as shown in the diagram.

1. Mark a line at the top and bottom of the ramp to indicate the start and finish lines. Make the distance from the start of the ramp to the start line slightly bigger than the trolley itself.
2. Measure the distance between the start and finish lines and record this.
3. Raise the ramp to a height of 10 cm, measure this to confirm. Measure the vertical distance between the finish line and the table.
4. Hold the trolley with its front touching the start line.
5. Simultaneously let go of the trolley and start the stopwatch being careful not to exert any force on the trolley.
6. Stop the stopwatch when the front of the trolley has reached the finish line. Record this time.
7. Repeat steps 5 to 7 three times with the same height.
8. Find the average of these values by adding the times and dividing by three. Record this Average.
9. Increase the height to 20cm, and repeat steps 4 to 9.
10. Continue this procedure of increasing the height and obtaining the average time until you have results for 6 different heights finishing at 60cm.

To calculate the speed of the trolley at the bottom of the ramp I will use one of the equations of motion:

S= (u+v) t

2

Rearranging this equation gives

2.S  = u+v

t

Where S (m) =distance travelled (distance between start and finish lines)

t (s) =time taken ( average time taken for the trolley to reach the finish line)

As u, the initial speed, will always be zero I will exclude it from the equation.

v (m.s-1)= final speed (The quantity to be calculated)

The final equation is:

2.S  = v

t

Conclusion

The accuracy of data wasn’t consistent throughout. There were great inconsistencies between the timings and distance measurements for example. If I was to repeat the experiment with the changes I have suggested, all major errors would have been eliminated. This would have definitely reduced the error and increased the reliability of the results. Any conclusions made would be much more valid.

The last three data points; at heights 0.20, 0.25 and 0.30 metres weren’t in accordance with the line of best fit; they differed greatly. As the times of the trolley reaching the bottom of the ramp decreased, the chance of error in reaction time would increase. The times for the highest inclination 0.3m, were around 0.75 seconds, in this short period of time my human error is likely to be amplified with late reaction times.

The first data point seems to be anomalous, however considering the fact that the last data point should have a lower value for speed, a new line of best fit would be closer to it.

Having considered the major errors caused by my timing, the evidence seems unreliable however I did take three values and average them, this does reduce the error. The other measurements were good and reliable. The difference between my value for the gradient and that predicted wasn’t greatly different, a difference of only 0.009. Even with my errors the results weren’t bad and I feel that conclusions can be drawn from them justifiably.

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