Skill Area P: Planning experimental procedures Introduction A trolley is pushed to the top of a ramp, the summit being 20 cm 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 30 cm 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 = mg (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 10 m / s 2 (or 9. 82 m / s 2 to be more precise). The onl 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 trolleys wheels, and air resistance.
There is no way I can control any of these factors, but they shouldnt 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 with Safety 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. Thats 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 well have to mind we dont accidentally attach a parachute to its back end... Water resistance just to point out the obvious, it wouldnt 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 1 cm-2 cm because the speed difference would be minor. Instead a more sensible range, lets say from 10 cm-50 cm, would be appropriate and should yield some interesting results. We could take readings every 10 cm, 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 200 g each time. Five or six is always a sensible number of results to obtain, so I will go up to about 1 kg. 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 10 cm) 20 cm ) 30 cm > Keeping weight constant 40 cm ) 50 cm ) Secondary Experiment three tests on each 200 g ) 400 g) 600 g > Keeping height constant 800 g) 1000 g ) 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 10 cm 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 10 cm.
Use the metre stick to check 12. Repeat from step 4 until you have obtained results for height from 10 cm through to 50 cm 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 10 cm using the metre stick 3. Add 200 g 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 200 g through to 1 kg 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. Ive 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 6000 j to climb the ladder so his potential energy at the top is 6000 j. 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 (3000 j 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 200 kg, 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 = 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 = x mass x velocity squared K. E = mv 2 Knowing this we can write: P. E = K. E mgh = mv 2 The formula can be simplified 20 h = v 2 SQRT (20 h) = 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 wont 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 formula, the shape of the graph v against h. As h increases uniformly, by lets say 10 cm 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 = mv 2 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 = v 2 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 2 m (sec) Velocity [distance / time ] (m / s ) Average speed (m / s ) 10 cm 3.
42 3. 58 3. 39 0. 58 0. 56 0. 59 0.
58 20 cm 2. 23 2. 15 2. 09 0. 9 0. 93 0.
9 0. 91 30 cm 1. 81 1. 75 1.
64 1. 11 1. 14 1. 22 1.
17 40 cm 1. 39 1. 52 1. 37 1. 43 1. 32 1.
46 1. 41 50 cm 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 ) 10 cm 1. 03 1. 04 1.
04 1. 04 20 cm 1. 66 1. 66 1. 66 1.
66 30 cm 2. 14 2. 14 2. 16 2.
15 40 cm 2. 51 2. 52 2. 52 2. 52 50 cm 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 2 m (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 conclusions Primary Experiment The graph clearly shows the increase in speed as the height of the ramp great ens, 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 heights the higher an object goes, the more gravitational potential energy it gains.
When it falls, its 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. 9 m / 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 = mv 2 Mass x gravity x height = x mass x velocity 2 Gravity x height = x velocity 2 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 17 th 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.
Galileos professor was highly sceptical about Galileos 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 earths 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 didnt 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 couldnt 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 0 g 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 wasnt 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.