trolley and the surface of the ramp can 'steal' some of the energy used to move the trolley and
convert it to heat instead. This can slow down the trolley, but only very slightly. To maintain the
same friction for all the results we should use the same material for the surface of the ramp, and
the same material for the wheel of the trolley. No grease should be added to lubricate any
equipment.
· Air resistance - there is very little we can do to control this factor, and its effects would be so
insignificant it may not matter. Basically, we just need to make sure we have the same trolley
and we'll have to mind we don't accidentally attach a parachute to its back end.
· Water resistance - just to point out the obvious, it wouldn't be recommended to conduct one
experiment in air and one in water...water is far denser than air and will create a stronger atomic
'barrier' which will drastically slow down the trolley.
With these points in mind it is essential that we must keep the same trolley, use the same ramp
and keep the mass constant in the primary experiment; and the height constant in the secondary
experiment. We will also have to keep the length of the runway the same, just so the trolley has
enough time to accelerate.
Ranges and amounts
To make this investigation successful, we must choose a sensible range, and amount, of readings
to record in order to come up with a useful and informative outcome. For example, in the
primary experiment it would be pointless to experiment with heights ranging from 1cm-2cm
because the speed difference would be minor. Instead a more sensible range, let's say from
10cm-50cm, would be appropriate and should yield some interesting results. We could take
readings every 10cm, and take a minimum of three readings on each height to work out an
average (this makes the end result more accurate).
For the secondary experiment, I chose to be working with weight going up by 200g each time.
Five or six is always a sensible number of results to obtain, so I will go up to about 1kg. Again,
a minimum of three readings should be taken on each weight for a mean average to be taken.
We may need to take results again if a factor that should be kept constant is accidentally
changed, or if the trolley is knocked for example. On the other hand, it may be interesting to
keep these anomalous results so they can be explained in the analysis. Below is a clear list of the
ranges and amounts in my two experiments.
Primary Experiment-three tests on each 10cm)
20cm )
30cm > Keeping weight constant
40cm )
50cm )
Secondary Experiment-three tests on each 200g )
400g )
600g > Keeping height constant
800g )
1000g )
Equipment
Before we begin, we will need a list of equipment for the experiment to ensure it all runs
smoothly:
Trolley - To roll down the ramp
Ramp - For the trolley to roll down
Metre Stick - To measure out 2 metres on the ramp
Chalk - To mark the start and finish lines
Stop Watch - To time the trolley
Barrier (bag) - To stop the trolley flying off the table
Books - For one side of the ramp to rest on, to increase the height of the ramp summit
Data Collection Sheet - To record our results on
Stationary - To write our results down with
Below is a diagram of how the equipment will be set up and used.
Using this equipment, we can easily obtain results with a high degree of accuracy. The usage of
books means we can increase the height by any amount because some books are thicker than
others are. We can get the height of the ramp at the start line almost exactly on the said
measurement by simply moving the pile of books forwards or backwards fractionally. Perhaps
manually timing the trolley with a stop-watch is not the most accurate way of recording the time
taken, but we may find a better alternative when we come to the practical.
Why?
From this experiment I expect to find out what factors affect the speed of a body when no
manual force is applied to them (i.e. pushing them). This experiment is being conducted to prove
the potential and kinetic energy formulae which, once completed, can be used to calculate
exactly the results of any situation using these theories. For example, the planning of a
rollercoaster - if we prove the formulae, they can be applied to find the exact speed of the train
at the bottom of a raised track x metres in height.
method
I have decided to produce a step-by-step guide for each experiment just to ensure that when
we actually come to conducting the practical work, it runs flawlessly. This will also help us
conduct fairer tests as we will be following the same set of steps each time we collect a result.
Primary Experiment
1. Set out equipment as shown in the diagram
2. Ensure the height at the start line (the summit of the ramp) is 10cm using the metre stick
3. Ensure there are no extra weights attached to the trolley
4. Hold the trolley with its front touching the start line
5. Simultaneously start the stop clock and release the trolley (be careful not to push it or exert
any extra force on it)
6. Stop the clock when the front of the trolley reaches the finish line
7. Record the time taken for the trolley to reach the finish, next to the relevant height, in a table
8. Repeat from step 4 twice more so you end up with three results for the same height then
continue onto step 9
9. Add all these results together and divide the answer by three to obtain the average.
10. Record this average in the table
11. By placing more books underneath the raised end of the ramp, increase the height at the
summit by 10cm. Use the metre stick to check
12. Repeat from step 4 until you have obtained results for height from 10cm through to 50cm
Secondary Experiment
1. Set out equipment as shown in the diagram
2. Ensure the height at the start line (the summit of the ramp) is 10cm using the metre stick
3. Add 200g of weights onto the trolley and affix them securely with tape in the middle, so they
do not interfere with the wheels.
4. Hold the trolley with its front touching the start line
5. Simultaneously start the stop clock and release the trolley (be careful not to push it or exert
any extra force on it)
6. Stop the clock when the front of the trolley reaches the finish line
7. Record the time taken for the trolley to reach the finish, next to the relevant weight, in a table
8. Repeat from step 4 twice more so you end up with three results for the same height then
continue onto step 9
9. Add all these results together and divide the answer by three to obtain the average.
10. Record this average in the table
11. Repeat from step 3 until you have results for weights 200g through to 1kg
By following these guidelines exactly, and not doing anything extra, we should conduct a very
fair test.
Predictions
Primary Experiment
As I mentioned in the Introduction, the experiment is based on the potential energy at the top of
the ramp being converted into kinetic energy at the bottom. I've taken this theory from the
source book 'Physics For You' (Keith Johnson) on page 115 where it simply explains the fact in
a basic diagram of a diver climbing to the top of a board. He uses 6000j to climb the ladder so
his potential energy at the top is 6000j. When he jumps off the board and falls, his potential
energy is proportionally converted into kinetic energy. Halfway down, there is equal potential
energy as kinetic (3000j each) and at the bottom all the potential energy has been converted
into kinetic energy. Using this theory, we can say:
Potential Energy (at the top) = Kinetic Energy (at the bottom)
Page 118 and 119 of the same book explains how to calculate potential and kinetic energy:
"A weight lifter is lifting a mass of 200kg, up to a height of 2 metres. We have already seen how
to calculate the potential energy of his weights:
Potential energy = work done
= weight x height lifted
But here on Earth, weight (in N) = mass x 10 so:
Gravitational P.E =Massgheight(joules)(kg)(N/kg)(m)(g has a different value on other
planets)"
The book also tells me the formula for kinetic energy is:
K.E = ½ x mass x velocity squared
K.E = ½mv2
Knowing this we can write:
P.E = K.E
mgh = ½mv2
The formula can be simplified
20h = v2
SQRT(20h) = v
This formula will give us the average velocity for the trolley going down a ramp of h metres high.
Once we have found this we can actually use the equation for average speed to find out how
long it will take the trolley to reach the finish line and actually produce a theoretical result prior
to conducting the experiment. Obviously, this won't be necessary for a simple prediction, but it
shows that the higher the ramp is raised, the higher the velocity of the trolley will be resulting in a
quicker time to reach the finish line. I can also predict from this formuIa, the shape of the graph
v against h. As h increases uniformly, by lets say 10cm each time, v will increase too - but not in
proportion. This is due to the square root in the formula that we have to use to find v. The higher
the height goes, the less gap there will be between the velocity of the present and previous
heights. The graph will look something like this:
Therefore, I predict
Increase in height of ramp = Increase in velocity of trolley
Secondary Experiment
Again, for the secondary experiment, we just need to examine the equation that states potential
energy at he top equals the kinetic energy at the bottom.
P.E = K.E
Mgh = K.E
Now looking at the equations at this stage, it seems sensible to say that a larger mass will result
in more kinetic energy, and hence a faster velocity. But lets look at the formula for kinetic
energy.
Mgh = ½mv2
Now we can see here that although a larger mass will indeed result in a larger amount of
potential, and therefore kinetic, energy it will not result in higher velocity. BOTH sides of the
equation contain mass, which simply means they cancel each other out.
Gh = ½v2
Therefore I predict that there will be no significant change in velocity when the weight of the
trolley is altered.
Skill Area O : Obtaining evidence
This section is mainly putting our planning into action, and hence is nearly all practical work so
not much written work will be produced.
Primary Experiment
When we came to conduct our experiment, we decided to alter our plan and do two
experiments. One using a stop-watch timer and one using a light gate to record the velocity of
the trolley for more accuracy.
Manually timing the experiment:
Height of runway (cm)Time taken to travel 2m (sec)Velocity [distance/time]
(m/s)Average speed
(m/s)10cm3.423.583.390.580.560.590.5820cm2.232.152.090.90.930.90.9130cm1.811.751
.641.111.141.221.1740cm1.391.521.371.431.321.461.4150cm1.241.251.281.611.61.561.5
9Using a light gate and computer software:
Height of runway (cm)Speed (m/s)Average speed
(m/s)10cm1.031.041.041.0420cm1.661.661.661.6630cm2.142.142.162.1540cm2.512.522.
522.5250cm2.852.852.852.85Secondary Experiment
As with the primary experiment, we used a light gate to collect another set of results.
Manually timing the experiment:
Added weight (g)Time taken to travel 2m (s)Velocity [distance/time] (m/s)Average
speed
(m/s)03.513.443.320.640.580.610.612002.332.172.130.860.920.940.914002.262.1520.88
0.9310.9460022.152.1610.930.930.958002.12.212.210.950.950.90.9410002.072.082.340.
970.960.860.9312002.22.312.290.910.870.870.89Using a light gate and computer software:
Added weights (g)Speed (m/s)Average speed
(m/s)01.621.661.51.62001.651.571.631.624001.641.61.651.636001.661.611.671.658001.
671.681.681.6810001.681.691.71.6912001.691.691.711.7We repeated ALL results three
times, even when using a light gate, to improve the accuracy of our experiment.
Skill Area A : Analysing evidence and drawing
conclusions
Primary Experiment
The graph clearly shows the increase in speed as the height of the ramp greatens, but not in a
proportional manner. The slight curve suggests that another force is acting on the trolley and not
permitting it to increase speed uniformly.
Again, when using the light gate, the results clearly show that there is a definite increase in speed
as the height of the ramp expands. The curve is slightly more prominent, and the peak speed
reached in this part of the experiment is almost double of that in the last.
Conclusion
My prediction was proved correct as the graphs clearly show that the speed does indeed
increase when the ramp is raised higher. This is due to the fact that more potential energy is
given to the trolley as it is raised higher - height is part of the formula that makes up P.E:
P.E = mgh
P.E = mass x gravity x height
So the higher an object goes, the more gravitational potential energy it gains. When it falls, it's
potential energy is converted into kinetic energy and; since energy can neither be created or
destroyed, only converted; it will move at a faster speed.
The vast difference in the manual timing speed and the light gate speed is probably due to
reaction time. The computer is able to record the speed far more accurately than we can.
So, to sum up, as you lift an object to a height, the chemical energy stored in you (which comes
from the food you eat) is converted into gravitational potential energy. Obviously, the higher you
lift the object, the more energy you are using and therefore the more potential energy the object
is gaining. Potential energy is converted into kinetic energy completely so the object when
released will move at a faster rate depending on how high it is lifted.
Height does affect the speed at which a trolley travels down a ramp
The graph shows no pattern. The speed stays roughly around the 0.9m/s mark except for a
suspected anomaly at the beginning.
The graph again shows no significant increase in speed as mass increases, but there is a slight
increase nevertheless. It is again almost double the speeds recorded in the manual timing
experiment.
Conclusion
The first graph shows a wavering line, going up and then down. This is expected from a manual
timing experiment as results should vary depending on our reaction time. There is an anomalous
result with no weights added - this was due to the fact that the trolley hit the side when travelling
down the ramp, losing a lot of its energy on friction and a bit on sound which drastically slowed
it down, as depicted in the graph. Other than this, the results tend to stay around the same
speed.
The second graph does show a little, but definite, increase in speed. This is caused by the
decrease in friction as more wheels are added. The extra force pushing down on the wheels
made them less prone to losing their energy on the surface of the ramp - but this effect is only
very slight. If we were to conduct this experiment in a place with no air resistance and no
friction, we would see that the speed of the trolley stayed perfectly constant as mass plays no
part in the equation of potential energy being converted into kinetic.
P.E = K.E
Mgh = ½mv2
Mass x gravity x height = ½ x mass x velocity2
Gravity x height = ½ x velocity2
Mass is cancelled out and theoretically has no impact on the speed of which an object travels
when it is given gravitational potential energy. Galileo proved this with his famous experiment-
"...In the 17th Century, Galileo was the genius who looked at this phenomenon with fresh eyes.
Legend has it that he climbed to the top of the leaning Tower of Pisa and dropped two cannon
balls over the side. One cannon ball was heavier than the other was. Galileo's professor was
highly sceptical about Galileo's idea and so Galileo had the professor lie at the bottom of the
tower with his ear to the ground! This was so that the professor could listen out for the two
thuds as one cannon ball hit the ground before the other one. The professor was dismayed to
only hear one thud - they had hit the ground at the same time!.." Taken from Bev Aldridge's
PGCE Notes
You may say a feather drops slower than a cannon ball, but it only flutters to the ground
because of air resistance. Air resistance acts on everything that moves through the air and is a
force that opposes motion, i.e. it makes a moving body slow down. Some shapes result in less
air resistance than others - a feather experiences much, and a coin very little. Thus when a coin
and a feather are dropped from the same height in a vacuum, they both hit the ground at the
same time.
This is an important principle in science. If air resistance is the same for two objects that are
dropped, they will gain speed at the same rate as each other even if one is much heavier than the
other is. So if they are dropped from the same height, they will hit the ground at the same time
as each other.
This is expressed scientifically by saying that acceleration due to gravity on the earth's
surface is constant.
Mass has no effect on the speed at which a trolley travels down a ramp.
Skill Area E: Evaluating Evidence
The experiments went very well and ran efficiently, thanks to the plan we had drawn out
beforehand. So well, we even had time to conduct another set of experiments using a light gate
and a computer package. This extra equipment made us sure that our results were accurate and
could be counted on. Thanks to the rapid speed of light, this device is extremely sensitive and
can measure speed to a very fine degree. For our experiment, we didn't require it to be as
accurate as the system allowed so we rounded the results off to three significant figures. With
our second set of results we were certain they were reliable and could be counted on.
Unfortunately, the same couldn't be said for the first set of experiments where we manually
timed the time the trolley took to travel down the ramp. Due to human error and reaction time,
these results could not be relied on completely, but did give us a rough idea. If we were to
conduct the experiment again, I would save time by just producing results using the computer
system with light gate.
There was one result that did not fit the pattern, and was too extreme to be our reaction time.
This was the result for 0g on the manually timed weight experiment. It was suspiciously lower
than the others were, and we agreed that it was the fact that the trolley hit the side wasting its
energy on friction. When we noticed the trolley had hit the side, we decided to take the result
anyway just to prove the point.
Thankfully, we had arranged to collect a sensible amount of results, which gave us enough
information to draw a conclusion from. I would not choose to change the amounts if I
conducted the experiment again because we managed to achieve maximum outcome in the time
allotted.
If I were to do this experiment again, I would experiment with different surfaces of ramp. I
wasn't expecting the mass to have any difference on the speed but, even with the light gate,
results showed a slight increase. I assume this was due to friction and would like to investigate
its properties. Also I would use a trolley than travelled in a straight line! The main problem we
found in our experiment was that the trolley kept swaying to the sides, creating a longer journey
and most of the time hitting the edge. This wasted a lot of time as we had to conduct the result
again. This also could have been due to uneven floor, so a spirit level may come in handy.
To extend this work, we could conduct Galileo type experiments, but take them a step further.
Perhaps, if we had the access to the right equipment, we could drop weights from different
heights in a vacuum (i.e. no air resistance), calculate the speed using light gates and see if it
produces theoretically perfect results. We could also try eliminating any other opposing forces,
such as friction, by polishing surfaces etc. and noticing if this changes the results.
To take the potential/kinetic energy element even further, we could look into elastic potential
energy and see if it works on the same principle as gravitational potential energy. A simple
experiment, such as pulling a trolley back against an elastic band and letting go to see how far it
goes, or what speed it goes at would be of interest. And we could also look into what
parameters effect the outcome, such as distance elastic is pulled, weight of trolley, type of
surface etc.
All these things would help further our progress in this area of physics and help our
understanding of the subject.