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The aim of this investigation is to devise and then execute an experiment to show the characteristics of a changing variable.

This coursework is based on acceleration. Acceleration is a measure of how quickly the velocity is changing. Acceleration can be calculated using the formula;

Change in velocity

Acceleration =

Time taken

Acceleration is measured in m/s˛

Velocity is measured in m/s

Time is measured in s

Another formula that involves acceleration is;

Force = Mass x Acceleration

If the mass is kept the same we can see that;1 • The bigger the force the greater the accelerationIf the resultant force is kept constant;2 • The bigger the mass the smaller the acceleration

Variables

• Mass of the trolley. This will affect its acceleration. Gravity is the force acting on the trolley, which is a constant. So, the second of the rules above will apply to this.

• Angle of the ramp. This will affect acceleration, but if the angle of the slope becomes greater than 90 degrees the angle of the ramp will have no effect as the trolley would now just be falling

• Friction. This will slow down the trolley because friction acts against gravity.

• Wind resistance. This will act in the same way as friction. Both will have greatest effect on the trolley when there is a large resultant force.

Wind resistance / Friction

Gravity

Which variable?

The variable that I have decided to investigate is the angle of the slope. This is because my results will be accurate and setting up the apparatus will be easy and precise.

Prediction

I predict that when the angle of the slope is between 1 and 45 degrees the acceleration of the trolley will increase quickly as the angle of the slope increases and then between 45 and 89 degrees the acceleration will still increase, but not as quickly, as the angle of the slope increases. When the angle of the slope is at 90 degrees the trolley will have reached its maximum acceleration. When the angle of the slope is greater than 90 degrees the trolley will no longer touch the slope and will just fall, so it will travel with the same acceleration. I have drawn a predicted graph comparing acceleration to angle of slope.

Apparatus and Recording results

To measure accurately the acceleration of the trolley we will use the laptop and light gates. The computer works out the acceleration and shows the results in m/s˛. Before it can do this we need to input measurements of the trolley length and the distance between the two light gates.

We will take results for slope angles of 5, 10, 15, 20, 25, and 30. To reduce the possibility of inaccurate results we will do the experiment five times for each slope angle.

To set the angle of the slope we will use trigonometry because it will be the most accurate method of doing this. If we want the angle to be a certain degree we will use the formula;

Sin x = O / H x = angle of slope

O = length of side opposite angle

H = length of hypotenuse

Fair test

To make it a fair test we will use the same trolley and ramp throughout the investigation. All of the variables listed before will be kept the same. However, we cannot control the wind resistance, but the experiment will be carried out inside so this shouldn’t be a great problem.

angle of slope

acceleration m/s˛

(degrees)

5 results

average

5

0.490

0.450

0.470

0.470

0.490

0.474

10

1.250

1.305

1.290

1.260

1.260

1.273

15

2.045

2.195

2.105

2.135

2.120

2.120

20

2.820

2.970

2.980

2.460

3.065

2.859

25

4.090

4.130

4.220

4.150

4.090

4.136

30

4.950

4.800

4.800

4.800

5.130

4.896

Results

The table (above) and the graph (below) show my results;

This graph is quite different from the one that I predicted. The curve of it isn’t nearly as steep, but it does show that the steeper the slope the faster the trolley accelerates.

My results have turned out very well and are all roughly the same. But as the ramp got steeper the results got more erratic (see results table). As the speeds increased the timing had to be more precise because the ramp was quite short (only one metre). For the smaller angles the speed of the trolley was quite slow and the time gaps (time it took to get from one light gate to the next) were quite big, but when the slope was steep the time gaps became much shorter. This problem could have been solved using a longer slope because the bigger the