Trolleys And Ramps Essay, Research Paper
Skill Area P:
Planning experimental procedures Introduction A trolley is pushed to the top of a ramp, the summit being
20cm from the ground, and then is released. It rolls all the way down the ramp,
of 2 metres, before it collides with the wall at the bottom. A couple of keen
scientists thought it would be interesting to record the time taken for the
trolley to reach the bottom and then calculate its average speed. They let the
trolley fall down the ramp two more times after that, just to make their results
more accurate. They also wanted to investigate if the height of the summit made
any difference to the average speed, so they raised the ramp to 30cm and pushed
the trolley down the ramp again and recorded the time.Basically I have been asked to act as the two enthusiastic
experts and test, as a primary objective, to see if the height of the summit
affects the average speed at which the trolley travels down the ramp. Based on my existing scientific knowledge, I know that
this experiment depends on a certain type of energy being converted into
another type. When the trolley is raised to the top of the ramp, it gains a
certain amount of potential energy ? this is converted into kinetic? (movement) energy as the trolley moves down
the slope. Too see what factors may affect the way the experiment turns out, it
may be useful to look at the formula for potential energy.P.E = mhg (where
m=mass, h=height and g=gravity)Obviously, the more potential energy the trolley has got,
the faster it will move down the ramp. So, theoretically, the only factors that
can affect this experiment are the height and the mass and the gravity. Since
we can only possibly conduct this experiment on Earth, the gravity will always
stay constant ? about 10m/s2 (or 9.82m/s2 to be more precise).
The only factors left are the variables I will be experimenting with in this
investigation·
Primary Experiment ? I will be investigating, by
varying the height the summit of the ramp is raised off the ground, if the
average speed increases or decreases. ·
Secondary Experiment ? I will be investigating if the
average speed changes by adding extra mass to the trolley.There will always be smaller forces that could slightly
affect the result, such as friction between the ramp and the trolley?s wheels,
and air resistance. There is no way I can control any of these factors, but
they shouldn?t affect the results so much as to give completely anomalous
readings for each experiment. Planning When planning my experiment, I will need to take into
consideration the following points: ·
Safety ·
Fair testing ·
Equipment ·
How many results I will take ·
What range of variables I will experiment withSafety With this straightforward experiment there is not much
that needs to be taken into consideration. No harmful substances are being
used, neither are flames, solvents, atomic-reactors or insurance salesmen so
all-in-all a relatively safe experiment. Obviously we will need to take
precautions when increasing the mass of the trolley and make sure that all the
weights are securely fixed to it by using sellotape, string etc. Especially
when the trolley reaches high speeds, the likelihood of weights falling off is
increased and this could be potentially harmful to an innocent on-looker. Also
at the bottom of the ramp some sort of barrier will need to be placed to
prevent damage to the trolley as it hurtles off the edge, or to thwart
potential harm to any unsuspecting pedestrian/small animal. That?s basically
it, the rest is all common sense.Fair Testing As with all scientific experiments, only one variable must
be altered at one time. All the rest must remain constant to ensure good
sensible results. By using present knowledge, I know that the following factors
can affect the outcome and must be controlled: ·
Height of ramp ? as this is included in the formula for
potential energy, the height of the ramp should affect the speed of the trolley
in some way. I will be modulating this variable in the primary experiment, but
it should be constrained to a single height in the secondary experiment. ·
Mass of trolley ? mass is also included in the formula
for potential energy and so could affect the speed of the trolley one way or
the other. As with height, this will be varied but only in the second
experiment. With the primary experiment we should constrain it simply by not
adding any weights to the trolley and always using the same trolley to collect
each result. ·
Gravity ? the last portion of the formula for potential
energy is gravity, which will affect the outcome if it is increased or decreased.
The way to maintain this factor is to simply stay on the same planet. ·
Friction ? I mentioned that the only factors that
should affect the outcome of the experiment would be mass, height and gravity -
because they make up the formula for the potential energy. But other factors
may use some of this energy when it is being converted into kinetic (movement)
energy as the trolley moves down the ramp.?
The friction between the wheels of the 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 withBelow 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 50cmSecondary
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 1kgBy following these guidelines exactly, and not doing
anything extra, we should conduct a very fair test.PredictionsPrimary 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 bee
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 liftedBut here on Earth, weight (in N) = mass x 10 so: Gravitational P.E = Mass g height (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 = ½mv2Knowing this we can write:P.E = K.E mgh = ½mv2 The formula can be
simplified 20h = v2 SQRT(20h) = vThis 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 evidenceThis 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) 10cm 3.42 3.58 3.39 0.58 0.56 0.59 0.58 20cm 2.23 2.15 2.09 0.9 0.93 0.9 0.91 30cm 1.81 1.75 1.64 1.11 1.14 1.22 1.17 40cm 1.39 1.52 1.37 1.43 1.32 1.46 1.41 50cm 1.24 1.25 1.28 1.61 1.6 1.56 1.59 Using a light gate and computer software: Height of runway (cm) Speed (m/s) Average speed (m/s) 10cm 1.03 1.04 1.04 1.04 20cm 1.66 1.66 1.66 1.66 30cm 2.14 2.14 2.16 2.15 40cm 2.51 2.52 2.52 2.52 50cm 2.85 2.85 2.85 2.85 Secondary
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) 0 3.51 3.44 3.32 0.64 0.58 0.61 0.61 200 2.33 2.17 2.13 0.86 0.92 0.94 0.91 400 2.26 2.15 2 0.88 0.93 1 0.94 600 2 2.15 2.16 1 0.93 0.93 0.95 800 2.1 2.21 2.21 0.95 0.95 0.9 0.94 1000 2.07 2.08 2.34 0.97 0.96 0.86 0.93 1200 2.2 2.31 2.29 0.91 0.87 0.87 0.89 Using a light gate and computer software: Added
weights (g) Speed
(m/s) Average
speed (m/s) 0 1.62 1.66 1.5 1.6 200 1.65 1.57 1.63 1.62 400 1.64 1.6 1.65 1.63 600 1.66 1.61 1.67 1.65 800 1.67 1.68 1.68 1.68 1000 1.68 1.69 1.7 1.69 1200 1.69 1.69 1.71 1.7 We 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 conclusionsPrimary 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 heightSo 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 velocity2Mass 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 NotesYou 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 EvidenceThe 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.Bibliography PHYSICS FOR YOU ? Keith Johnson WESTMINSTER COLLEGE RESOURCE PGCE NOTES ? Bev Aldridge FORCES IN ACTION