Investigation on ‘The Law of Conservation of Energy’

The Law of Conservation of Energy states that energy can neither be created nor destroyed: it is always changed from one form to another.

If an object is raised above the ground it acquires Gravitational Potential Energy (GPE). The amount of GPE depends upon the mass (m), the force of gravity (g) and the vertical height the object is lifted (h), where:

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GPE (in joules) = mass (in kilograms) x force of gravity (10N/kg) x height (in metres)

or

GPE = mph

If an object is allowed to fall under the influence of gravity, it acquires Kinetic Energy (KE). The amount of KE depends upon the mass (m) and the velocity (v) where:

KE (in joules) = 1/2 mass (in kilograms) x velocity2 (in metres per second)

or

KE = 1/2mv2

Plan

I have to use a dynamics trolley in order to investigate and prove the Law of Conservation of Energy. To do this I will set up a ramp and a let the dynamics trolley roll down it, measuring the energy at the start, and at the end of its movement.

The Law of Conservation of Energy states that energy is not lost when we do something, it is merely changed from one form to another. This should mean that the energy at the start of our movement and the energy at the end, should be the same. In order to measure the energy I will need to know several key factors: the mass of the trolley, the force of gravity, the height of the trolley at the start of each run, and the velocity at which the trolley is travelling (at the end of the run). We need the velocity at the end of the run, because this will be the moment when all GPE is changed into KE.

Here is a table of the key factors we need to know, and their values:

Factor

Value

Weight of trolley

0.540kg

Force of gravity

10N/kg

Height of ramp

Variable

Velocity of trolley

Variable

The height and the velocity have been shown as variable. I will vary the height of the ramp in order to gain several different results (giving a more accurate result). The velocity of the trolley is also variable, as as the height changes, so too will the velocity of the trolley at the end of each run.

I will work out the velocity of the ramp by using a piece of ticker tape attached to the end of the trolley. The distance between the dots, at the point of the end of the ramp, will allow me to work out the velocity at the end of the run. To find the point on the tape where the ramp ends, I will simply deduct the length of the ramp (2.55meters) from the start of the ticker tape marking.

The velocity of the trolley depends upon the distance (d) and the time (t) where:

Velocity = Distance (in meters)

Time (in seconds)

or

v = d

t

I will use the ticker tape to obtain the measurements accurately, as we know that the time in between each ticker tape dot in 1/50 of a second. The distance will vary.

For example, if the distance in between the dots was 5cm, then we substitute that into the equation to get:

Velocity = 0.05m

0.02s

This gives us a velocity of 2.5m/s. I can then use this (and the mass) to find the KE of the trolley.

Results

Note: All units have been converted so that they fit the original equation. (e.g. centimetres to meters)

Height of ramp (h)

10cm

20cm

30cm

GPE at start (in J)

0.540 x 10 x 0.1 = 0.54

0.540 x 10 x 0.2 = 1.08

0.540 x 10 x 0.3 = 1.62

Distance between dots (d)

2.5cm

3.5cm

4.5cm

Velocity of trolley (in m/s)

0.025 / 0.02 = 1.25

0.035 / 0.02 = 1.75

0.045 / 0.02 = 2.25

KE at end (in J to 2d.p)

0.540 / 2 x 1.252 = 0.42

0.540 / 2 x 1.752 = 0.83

0.540 / 2 x 2.252 = 1.37

40cm

50cm

0.540 x 10 x 0.4 = 2.16

0.540 x 10 x 0.5 = 2.7

5.5cm

6.5cm

0.055 / 0.02 = 2.75

0.065 / 0.02 = 3.25

0.540 / 2 x 2.752 = 2.04

0.540 / 2 x 3.252 = 2.85

Analysing

Here is a graph to show the relationship between the height of the ramp and the trolley velocity.

This graph shows us that as the height of the ramp increases then so does the velocity of the trolley at the end of the ramp. This should meant that the gradient of the graph will be equal to the acceleration of the trolley per 10cm height increase.

This is the working of the gradient:

0.5

10 = 0.05

This means that as the height of the ramp increases by 10cm, the velocity of the trolley will increase by 0.5m/s. This will eventually stop as the trolley end up going at maximum velocity before the end of the ramp. At this point we would see the graph stop rising and level off.

My results clearly show that the energy at the end is not the same as the energy at the start. This could be because: a) The Law of Conservation of Energy is wrong (this is extremely unlikely!)

b) energy has been converted by the trolley as it has moved down the ramp.

I think that energy has definitely been converted, because there was sound from the trolley as it was moving down the ramp, this must have taken energy to create. Also, the air resistance would have slowed the trolley down as it was moving, this would have taken energy to surpass. Friction from the bearings in the trolleys wheels and the ramp would also have converted energy into heat, in turn slowing the trolley down. I am sure that there are other factors that may have affected the trolley, but this does show that the trolley is losing energy as it moves down the ramp.

From my results I have decided that the result when the ramp is at 50cm must be wrong, due to the fact that the KE is higher then the GPE. I am unsure as to why this is, but it doesn’t affect my experiment greatly as I still have evidence to show that energy has been converted.

Evaluation

I think that there are many factors which may have affected my results, and could have caused my results to be inaccurate. The result where the height is 50cm is a good example of this inaccuracy, as I know that there should not be a higher KE than GPE. The only explanation I can come to for this result is that there was a gust of wind which pushed the trolley, or that when I was releasing it I accidentally pushed it slightly. There are factors that you could change in order to obtain a more accurate result these include:

1) Do the experiment in a vacuum. This would avoid any chance of wind affecting the trolley, and also eliminate air resistance.

2) Make the wheels and bearings of the trolley so smooth that there is no friction. This is highly implausible, but it would increase the accuracy of the result.

3) Use a laser timing system so that the ticker tape cannot cause friction as it passes through the ticker timer, or air resistance as it lags behind the trolley.

4) Measure all results to a large degree of accuracy. This would obviously improve results.

All these methods could be used, although they are very extreme and somewhat irregular. They would also need very sophisticated equipment, which could probably be used for a better purpose.

Considering the equipment I used, and the circumstances in which I worked, I believe that my results are adequate to prove that energy is converted from one form to many others, as the trolley moves down the ramp.

Mike Games GCSE Physics Coursework

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