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 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 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