Acceleration of a Trolley


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Acceleration of a Trolley


Plan

An unbalanced force causes an object to accelerate. The acceleration
happens in the same direction as the resultant (or unbalanced) force.
The size of this depends on the mass of the object and the size of the
force.

The force on a small object is bigger than the same force acting on a
bigger object.

If the mass stays the same but the force gets bigger, the acceleration
also increases.

The equation to find acceleration is: [IMAGE][IMAGE] when [IMAGE]=
acceleration, [IMAGE]= velocity at the end, [IMAGE]= velocity at the
start, and [IMAGE]= time

The variables which could affect the acceleration of a trolley down a
ramp are:

The mass of the trolley, - (the size of the trolley), if the same
force acts on a bigger object it will accelerate less than that force
on a smaller object.

The continuous force, - (how much the object is pushed), the bigger
the push or force, the bigger the acceleration.

The gradient of the slope, - (the height of the slope that the object
moves down), the bigger the gradient, the bigger the acceleration will
be as the object travels down it, because less friction acts against
an object which travels down a steeper slope and friction reduces the
acceleration of an object.

The variable which I have chosen to investigate is the gradient of the
slope. I think that out of all the variables, this is the one which is
easiest to measure and to change accurately, ensuring a wide variety
of reliable data.

I predict that the as I increase the height of the slope (or the angle
between the floor and the ramp), the acceleration will increase, due
to a more direct force from gravity caused by less friction on a
steeper slope.

[IMAGE]

Light gate

Light gate

Trolley

Angle between floor and ramp

Ramp

I will measure the acceleration of the trolley by running it down a

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ramp, through a light gate. The light gate is connected to a computer
which monitors the acceleration by measuring the speed of the
interrupt cards on the trolley as they pass through the light gate.

I will need to measure the height of the ramp for each experiment; the
computer will measure the acceleration.

The heights I will be measuring are:

10cm,15cm, 20cm, 25cm, 30cm, 35cm, 40cm

I will do each experiment three times and take the average result for
each height to ensure an accurate result.

To make sure that it is a fair test, I will make sure that the back
wheels of the trolley are always 60cm from the light gate at the
beginning of each experiment. The height will always be measured
accurately with a cm ruler.

The computer program which measures the acceleration of the trolley
down the slope is accurate to 0.01 m/s/s. This will ensure that my
results are accurate.

I will measure the acceleration of the trolley at each height three
times, and then take the most sensible result or average, excluding
anomalies and therefore ensuring reliable results.

Obtaining Evidence

Results of acceleration of a trolley experiment

Height (cm)

Acceleration (m/s/s)

Average Acceleration

Angle between floor and ramp

10

0.27

10

0.24

0.26

3

10

0.26

15

0.75

15

0.70

0.75

4.7

15

0.75

20

1.38

20

1.06

1.36

6.2

20

1.34

25

1.94

25

1.57

1.76

7.8

25

1.78

30

2.45

30

2.42

2.44

9.3

30

3.10

35

3.21

35

2.70

2.79

10.9

35

2.88

40

2.93

40

2.67

2.80

12.5

40

3.01

There were 5 (highlighted in red) anomalous results in the 21
experiments carried out. I used my judgement to decide on a
representational average which excluded these. Averaging all the
results would mean that they would not be as accurate; the anomalies
would throw off the balance and create an inaccurate average.

Analysing Evidence

[IMAGE]

This graph shows how the acceleration increases as the slope gets
steeper but by less each time. I predict that if I had continued to
increase the slope past 40cm, there would be more of a curve as the
acceleration would begin to converge, and not increase by so much each
time.

I thought a more accurate way of measuring the increase in
acceleration would be to look at the angle between the floor and the
ramp. To work this out I used the mathematical formula:[IMAGE][IMAGE]

[IMAGE]

This graph shows the correlation between the angle and the height. I
was expecting more of a curve and I think that if I had again gone
further than 40cms I would have been able to draw more from this
graph.

Next I compared the angle to the acceleration to see if it was a more
accurate way of measuring the increase in acceleration as predicted.

[IMAGE]

It is clear from this graph that the points roughly follow a straight
line although unfortunately I don't think that this is any more
accurate than the graph comparing height to acceleration.

Although my results weren't exactly as I predicted, (I expected more
of a curve on the graph involving height and the angle), it is still
clear that as the height of the ramp increased, so did the
acceleration of the trolley. This is due to the decreasing amount of
frictional force acting on the trolley as the gradient increases
leading to a greater resultant force and faster acceleration.

Evaluating Evidence

There were a number of anomalous results in my experiments. Although I
listed them in my table of results, I was careful not to include them
when taking an average acceleration for each height. I could see that
doing this would make the average inaccurate and used my judgement to
take a reliable average.

The computer which measures the acceleration is very accurate and
therefore I think that the anomalies must have been caused by the
method.

The trolley could have started too far back or forwards or maybe could
have hit the light gate on its way through. The height of the ramp,
although kept at the same for each set of 3 experiments could be
measured more precisely for more accurate results.

The fact that each of my experiments was done three times increases
the reliability of my results. I think that it is important to do each
experiment three times. That way, if you have very conflicting
results, it is easier to see which the anomaly is and which the two
reliable results are.

If I was going to re-do my experiments I would change a number of
things. I would do more heights, increasing it to 60 or 70cms. That
way, it is easier to see patterns on and draw conclusions from your
graphs. I would be careful to keep all other variables, apart from the
height, the same at all times. I would also try and be more precise
about measuring the height of the ramp. These would make the
experiment generally more accurate.

Another idea I had on how to perhaps make the experiment more accurate
would be to use set angles rather than set heights. E.g. 5 degrees, 10
degrees, 15 degrees, and work out the height using trigonometry
accordingly.





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