# Upon what does the final speed of a trolley depend as it goes down a ramp? An in-depth plan and scientific prediction including variable discussion for the said experiment.

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• Published: January 10, 2004

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Upon what does the final speed of a trolley depend?

Aim- The Aim of this investigation is to discover how certain variables affect the final speed of a trolley. I will investigate this using an elevated ramp and a trolley to down it. I will investigate the relationship between the height of a ramp (which a trolley is rolled down) and the trolley's final speed as it comes off the ramp.

Hypothesis- I predict that as the height of the ramp is increased the final speed of the trolley will also be increased: this can be both measured and easily seen. A trolley accelerates down a ramp due to the force of gravity pulling it towards Earth. If the ramp is heightened, the trolley is therefore higher.

Gravitational potential energy = Weight x Height

Via this equation we see that gravitational potential energy is higher: the trolley's weight does not change but its height is more so it has more gravitational potential energy. It is gravitational potential energy that accelerates the trolley down the slope because over the course of the slope gravitational potential energy is converted into kinetic energy. Therefore if there is more gravitational potential energy available to be converted into kinetic energy the trolley will have more kinetic energy and thus its final speed will be faster.

I further predict that the Height of the ramp will be directly proportional to the final speed of the trolley squared.

Kinetic energy = ½ mass x speed"

From this we see that the kinetic energy of the trolley is dependent upon its speed. The trolley obtains its kinetic energy as it goes down the slope solely due to gravitational potential energy; as explained above. So, in this case:

Kinetic energy = Gravitational potential energy

Therefore:

Gravitational potential energy = ½ mass x speed"

The mass of the trolley remains does not change at all during the experiment. Therefore speed" is dependent on Gravitational potential energy; i.e. the Height of the ramp is higher. Therefore as the ramp is raised, speed" will increase proportionately to the extra Gravitational potential energy the trolley is given by its increased elevation. Therefore a graph should show that Gravitational potential energy is proportional to speed" in this experiment.

Gradient- I expect a gradient of 1:20 to be achieved on graphs drawn: that is, using standard S.I. units of seconds and metres to calculate the height of the ramp and the speed of the trolley, I expect an increase of the height of the ramp by a certain amount to make the Final speed of the trolley squared to increase by twenty times that amount.

As shown and explained above:

Gravitational potential energy = ½ mass x speed"

Since:

Gravitational potential energy= Mass x Height x gravitational field strength

Since the gravitational field strength on Earth is (approximated to) 10N/kg:

Mass x Height x 10 = ½ mass x speed"

Dividing both sides by Mass we see that:

Height x 10 = ½ speed"

Therefore:

20 x Height = speed"

Therefore an increase of Height of the ramp by one metre will consequently cause an increase in the final speed of the trolley squared (in (metres/second) ") by 20 giving a gradient of 1:20 on the graph (assuming that Height is plotted in Metres and Final speed of the trolley squared is plotted in (m/s) ".

Variables- There are various variables in this experiment all affecting a trolley's final speed as it comes off a ramp:

Control

Friction of ramp

Length of ramp used

Trolley used

Gravity

Independent

Height of the ramp

Dependent

Final speed of the trolley

-Friction of the ramp. A ramp which produces more friction as a trolley goes down it with invariably slow the trolley; affecting its final speed. This will be controlled in the main experiment by using the same ramp.

-Trolley used. Differing trolleys will have differing speeds and accelerations down a ramp due to their size, mass and the friction produced in...