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The factors which affect the speed of a ball rolling down a slope set at different heights
Introduction
In this piece of coursework, I am going to be measuring the speed at which a ball rolls down a ramp. From the results I will record, I will be able to work out the speed of the ball, the Gravitational potential energy of the ball at different heights, the Kinetic energy of the ball, and the Friction force which will be acting upon it.
The ways in which I will obtain these results, is by using the following Formulae:
Mean Speed ( m/s ) = Distance traveled ( Metres )
Mean Time Taken ( Seconds )
Weight ( N ) = Mass ( Kg ) X Gravity ( N / Kg )
Gravitational potential energy ( J ) = Weight ( N ) X Change in Height ( m )
Kinetic Energy ( J ) = 1/2 X Mass ( Kg ) X Speed2 ( m/s )2
Friction Force ( J ) = G.P.E. ( J ) - K.E. ( J )
I will describe how I will carry out the experiment safely and accurately, so that I can make sure that when i accualy do the experiment no-one will get injured and I will be able to get accurate results. Using the formulae above, I will be able to work out all of the answers which I need. I will represent my results in tables and graphs, so that they are easyer to see.
Planning
Before I could start my experiment, I had to plan out my experiment completely, so that I could make sure that I was making a fair, safe and accurate experiment. I thought about all of the possible factors which would affect my results, and made shore that none of these variables would affect the safety of my experiment.
One of my main concerns was on how to keep my experiment a fair test. I achieved this, by writing down all of the possible variables which I could have change, but only choosing one of them to actually change. The factors that I could have changed, were:
· Weight of the ball,
· Size of the ball,
· Texture of the ball,
· Length of the ramp,
· Smoothness of the ramp, and the
· Height / Angle of the ramp.
I decided to change the height of the ramp, and therefore the angle of the ramp. I chose this variable, because this would allow me to work out the gravitational potential energy at the start of the experiment. Therefore, this would allow me to work out the kinetic energy of the ball, when it gets to the end of the ramp.
I also decided that I would make sure, while I was carrying out my experiment, that none of the other variables would change. If I managed to succeed in doing this, then my experiment will be a fair and accurate test. The way in which I will keep the test fair, is by using the same equipment all the way through my experiment. Theoretically this should make the results which I get accurate, and as close to the predicted answers as they possibly can using the equipment available to me.
The number of measurements will be very important in my experiment, because the answers should be able to give me an average of the results, so that my actual answers will be as close to the real ones as possible. Therefore, I have decided to repeat the experiment another five times at each height, so that the average of my answers will get more accurate. Carrying out the experiment a total of six times, will also show me any obviously wrong answers, which I will probably get using the equipment I have available. If I was to use more precise equipment, I would still need to repeat the experiment at least six times, just to make shore that no mistakes are made. I will also use five different heights during my experiment, so that I can work out if my prediction is correct.
I will use the same ramp for all of my experiments, the length of which will be 150cm. The heights of the ramps which I will be using are:
· 25cm,
· 35cm,
· 45cm,
· 55cm, and
· 65cm.
I have decided to use these values, so there is an even spread between the heights, and so that these values should represent the increase in speed for the increase in gravitational potential energy.
The different types of apparatus I will need to use, are:
· Clamp Stand,
· Flat, smooth piece of wood,
· Ball ( Squash Ball ),
· Stop Watch,
· Metre Ruler,
I have decided to use these pieces of equipment, so that I can get a detailed, and accurate set of values. While these pieces of equipment will be adequate for the results that I will be getting, if I, or a professional scientist was going to do this experiment again to get a more precise set of values, we would need more accurate timing equipment. Instead of using a stop watch, we could use two photo-electric cells, connected to an electronic stop watch, or a computer. This would start the watch when the ball is set off, and stop the watch when the ball passes the second light beam. This would greatly increase the accuracy of my results, because there wouldn’t be a delay when I am reacting.
I could also use a flat, smooth metal ramp, so the ball wont be as affected by friction. There are probably a lot more scientific ways of measuring the time it take for a ball to travel down a ramp, but using the equipment and knowledge which I have available, this is the best experiment that I can do.
Safety
One of my main concerns I will need to think about before I start my experiment, is safety. The main safety risk is the plank of wood falling, and injuring somebody. To prevent this happening, I will fix the top of the ramp in position using a stable metal clamp stand. I will also tape the bottom of the ramp to the floor to prevent it slipping. There are no other significant safety problems associated with this experiment
Results
I will record my results in a table, so that the information can be seen clearly and easily. The information I will record, is the height of the ramp, and the time taken for each repetition to be done. I will then extend my results, to show the angle of the ramp and the average speed of the ball over the distance travelled.
Prediction
I predict that the steeper the ramp is, the faster the ball will travel. I also predict that the rate of increase, of the speed of the ball, will decrease as the ramp gets steeper. Thirdly I predict that the speed of the ball will be proportional to angle of the ramp.
The reason for my first prediction is that I know that, if the ramp is horizontal, then the ball can only have a speed of zero; and if the ramp is vertical, then the ball will fall freely at its maximum speed. This gives me a range of speeds the ball could have. I can calculate the theoretical free-fall speed in the following way:
Distance ( m ) = 1/2 X Acceleration ( m/s2 ) X Time2 ( Seconds2 )
1.5m = 1/2 X 9.81m/s2 X T2
T2 = 2 X 1.5 / 9.81 = 3 / 9.81 = 0.3058
T = 0.553 Seconds
Mean Speed ( m/s ) = Distance ( m ) / Time ( s )
S = 1.5m / 0.553sec = 2.71 m/s
I can work out the mean speeds of the ball going down the ramp, using a simple equation.
Mean Speed ( m/s ) = Distance travelled ( Metres )
Mean Time Taken ( Seconds )
I will use the mean times ( from my six results ) to give a more accurate answer.
The reason for my second prediction is that I think that, the steeper the ramp is, the less influence friction will have on the ball's speed. If the ramp was nearly vertical there would not be much difference to the results for a vertical ramp. However if the ramp was nearly horizontal the ball would move quite slowly.
For my third prediction, I think that the speed of the ball will be proportional to the angle of the ramp. I think this because when the ramp has a small angle, the speed is quite slow, but when the angle is larger, the ball has a faster speed.
Obtaining
After I had checked my planning section with my teacher, I set about doing the experiment. I collected my equipment from the pieces supplied to us, and set them up as shows in the diagram. I kept the whole experiment safe and fair, by following my plan and by thinking about everything I did.
When I was putting the ramp together, I made a mark on the top of the piece of wood, to mark where 150cm was from the bottom of the ramp. I did this, so that I would be able to start the ball rolling from the same position on the ramp each time.
The first measurement I was going to take, was with the mark at a height of 25cm above the floor. I used a ruler, to set the starting position of the ramp to the right height, so that we would get accurate results. I used blue-tack to secure the bottom of the ramp, so that it wouldn't move, and I also place a large cardboard box just past the end of the ramp so that the ball wouldn't roll all over the classroom. Next I made sure that the clamp stand was secure, so that it wouldn't cause any injuries; and then I was ready to begin my first experiment.
I picked up the ball which I was going to use, a squash ball with a mass of 23.75g and a diameter of 3.8cm, and held it on the line which I drew earlier. I picked up the stop watch in my other hand, and was ready to set the ball rolling. I let go of the ball, and pressed the start button on the stop watch at the same time. As soon as the ball left the ramp, 150cm away, I pressed the stop button on the stop watch. I wrote down the result in a table ( see results ), and then repeated the experiment again and again, until I had six results for that height.
When I had got my six results for that height, I reset the apparatus, but this time I set the height of the ramp to 35cm. I used the same apparatus for this, and all of the other experiments I did, as I did for the last set of experiments. When I had six results of this height, I reset the apparatus to 45cm. I kept repeating the experiment six times for each height, so that I could work out an average for my results. After I had my results for a height of 45cm, I did experiments to get six results for heights of 55cm, 65cm and 75cm.
After I had finished my experiments, I carefully dismantled the apparatus, so that it wouldn't injure anyone.
Results and Analysis
Using the methods I described above, I obtained the results shown in Table 1 below. These show my results for ramp heights of:
· 25cm,
· 35cm,
· 45cm,
· 55cm
· 65cm, and
· 75cm;
and give my six results for each height, together with the calculated mean time taken.
Table 1
Height of ramp 1st measurement 2nd measurement 3rd measurement 4th measurement 5th measurement 6th measurement Mean time taken seconds
25cm 1.65 1.54 1.41 1.53 1.57 1.49 1.53
35cm 1.31 1.34 1.28 1.31 1.33 1.31 1.31
45cm 1.19 1.22 1.13 1.18 1.26 1.21 1.20
55cm 1.04 1.07 1.12 1.09 1.05 1.09 1.08
65cm 0.97 1.00 0.98 0.99 1.03 0.95 0.99
75cm 0.86 0.95 0.94 0.89 0.94 0.9 0.91
From these results, I have prepared graphs ( see fig 1, 2, 3, 4 and 5 ) which show the following relationships ( including lines of best fit where appropriate ):
· different times the ball took to travel down from differen heights;
· average times the ball took to travel down from different heights;
· mean speed of the ball, compaired to the height of the ramp; and
· actual mean speed of the ball, compared to my predicted speeds
· relationship of G.P.E., K.E. and Friction..
These results and graphs show that the time taken by the ball to roll down a slope of 150cm decreases as the height of the ramp increases. From graphs 1 and 2, it can be seen clearly that the difference in time taken is also decreasing for each increase in height. Graph 2 shows that the line of best fit is a smooth curve for the range of heights I have used.
When the times are converted in to speeds, the relationship shown in Graph 3 between speed and height, becomes a straight line of best fit. This means that the speed of the ball is increasing uniformly across the range measured. When this is compared to the stationery and freefall speeds of the ball, as shown in Graph 4, it is apparent that the straight line graph can't be extended to either the zero or maximum speeds. It is also apparent that my actual results do not lie on the theoretical smooth curve I predicted.
The theoretical curve does not make any allowance for friction, which is present in my actual experiments. The difference between my straight line graph and the theoretical curve must therefore be the result of friction forces.
Using the information gathered in my experiments it is possible to calculate the Gravitational Potential Energy and Kinetic Energy of the ball at the top and bottom of the slope respectively for each height. The equations are:
Gravitational potential energy ( J ) = Weight ( N ) X Change in Height ( m )
Kinetic Energy ( J ) = 1/2 X Mass ( Kg ) X Speed2 ( m/s )2
Friction Force ( J ) = G.P.E. ( J ) - K.E. ( J )
The results of these calculations are shown in Table 2, and are also shown on Graph 5.
Table 2
Heights of ramp G.P.E. K.E. Friction KE / GPE
25cm 0.059375 0.011405 0.04797 0.192084
35cm 0.083125 0.015705 0.06742 0.188932
45cm 0.106875 0.018555 0.08832 0.173614
55cm 0.130625 0.022944 0.107681 0.175648
65cm 0.154385 0.027436 0.126949 0.177712
75cm 0.178125 0.032329 0.145796 0.181496
From the graph it is apparent that the G.P.E. increases linearly with the height of the ramp. Similarly the K.E. increases linearly in line with my recorded results. The value for the K.E. is only about 18% of the value of the G.P.E. and the remainder is accounted for by friction. This means that the energy lost through friction is far greater than that gained by the increase in speed.
Conclusions and Evaluation
In this experiment I have tested the relationship between the speed of a ball rolling down a slope and the height of that slope. From this I have been able to calculate the changes in Gravitational Potential Energy, Kinetic Energy and Friction that occur as the height of the ramp, and hence the speed of the ball, varies.
My first prediction was that the speed of the ball would increase as the height of the ramp increase. I have proved that this is the case as my results and graphs demonstrate.
Secondly I predicted that the rate of increase of the speed of the ball would decrease as the height of the ramp increased. This prediction was not correct, as the rate of increase measured was constant over the range of heights I used. This difference was due to the effects of friction on the ball.
My third prediction was not correct either. I predicted that the speed of the ball would be proportional to the angle of the ramp. My results showed that the speed was actually proportional to the height of the ramp rather than the angle, as the graph was a straight line over the range of values I measured. This was again due to the effects of friction on the ball.
I have also calculated the ratio of K.E. to G.P.E. for the range of values I obtained. This shows that the ratio varies slightly across the range, but reduces and then increases. From this I conclude that my values were taken across the range of values for which friction was a proportionately a maximum. This may be the reason that I obtained a straight line graph for my results of mean speed against height of ramp. My results may not have been accurate enough to produce the true shape of the graph that I expected as my second prediction. The same effect could have also been responsible for my third prediction not being proved.
To be able to confirm the true relationship between G.P.E., K.E. and Friction, I would need to be able to measure the time the ball took to travel down the ramp far more accurately. This would best be done electronically to guarantee precise results. This would avoid problems resulting from my speed of reaction at both the start and finish of the tests. The steeper the ramp, and hence the shorter the time, the more critical my reaction time becomes.
My calculations have also assumed that the ball is accelerating for the whole time it is rolling down the slope. There was no way of telling if this was the case in my experiments. If I were to repeat the experiment using shallower slopes , the times may be more accurate (because of the longer time), but the results may be inaccurate because the ball had reached its terminal velocity before reaching the end of the slope. To ensure that the experiments were truly accurate I would need to find a way of making sure that the ball was still accelerating. One way would be to use a shorter ramp, but this would also reduce the times, and make accurate time keeping even more essential.
Another way would be to use a smoother ramp and ball. This would reduce friction and increase the speed of the ball and therefore its Kinetic Energy. The time taken to roll down the slope would also be less, requiring more accurate time keeping.
In my opinion I have carried out the experiment as safely and as accurately as I possibly could with the equipment available to me. I would need to have more accurate equipment, particularly for measuring time, to be able to produce a better set of results and more accurate conclusions.
Word Count: 3186
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