Investigating the Factors that Affect the Acceleration of a Ball Bearing Down a Ramp
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bearing down a ramp. I will measure how long the ball bearing takes to roll down a ramp, and my other variable will be to measure the final velocity of the ball bearing rolling down the ramp. Using this information I will then be able to work out the acceleration of the ball bearing down the ramp. I will be able to work out the velocity of the ball bearing, and therefore be able to work out the acceleration using a different formula above. I will conduct two experiments and for both there will be only one variable with everything else fixed. In the first experiment, my variable will be the mass of the ball bearing which rolls down the ramp. In the second experiment, I will keep the mass of the ball bearing the same but change the angle of the ramp that the ball bearing rolls down. CHANGING THE MASS OF THE BALL In this experiment the only factor I will change will be the mass of the ball bearing which rolls down the ramp. Apparatus To do the experiment, I will need to use the following equipment: a plastic ramp, a stand, a clamp, a nail, a metre rule, a selection of ball bearings with varied masses, How to Cite this Page
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four metal electrodes, four crocodile clips, four wires and a stopclock. The ramp will be set up originally to get a 5° angle. I have worked out using the sine function that the start of the ramp needs to be 10.9cm off the ground. The ball bearing will be released from the top of the ramp and will roll down. The ball bearing will be rolled down twice. On the first roll, the final velocity of the ball bearing as it rolls down the ramp will be measured. This will be measured by connecting wires to the stopclock and set points on the ramp. The electrodes are placed close together either side of the ramp. As the metal ball rolls over them the circuit is completed and starts the stopclock. As it then rolls over the second set, it again completes the circuit and stops the clock. I must use an insulator for a ramp because if I used a conductor the electricity would run from one electrode, through the ramp to the other electrode and start the stopclock. For this reason, I am using a plastic ramp. This is much more accurate than me timing the ball. I will take three readings, and in the end take the average. I will then work out the final velocity by using the formula below. I will take three readings, and in the end take the average. Distance travelled in a given direction (m) Time taken (s) 1. Velocity (m.s1) = On the second roll, the time it takes to roll from the top to the bottom will be measured. As the metal ball rolls over the electrodes at the top, it completes the circuit and starts the stopclock. As it then rolls over the second set of electrodes, it again completes the circuit and stops the clock. Again I will take three readings, and in the end take the average. I already know the initial velocity to be zero, so using the final velocity and the time it takes the ball to roll down the ramp; I can work out the acceleration of the ball. I can work this out using the formula below. Change in velocity (m.s1) 2. Acceleration (m.s2) = Time taken for the change (s) Once I have worked out the acceleration for one ball, a different ball with a different mass will then be used and the procedure repeated. I will do this with four balls with different masses, as I believe I will be able to obtain a good graph with the amount of results. I will use the masses 6.06g, 7.30g, 8.63g and 9.07g. From my preliminary work, these seemed like a good range of masses to use. To make it a fair test I will need to release each ball from the same height on the ramp. The further the ball falls, the faster it will go so if I release them from different heights the acceleration of the balls will be different. The most important thing to keep the same is the angle of the ramp, I will keep it at 5°. If the angle changes then the acceleration of the ball bearing will change automatically. I have chosen to use the angle of 5° because from my preliminary work, which I carried out before the experiment, it seemed like a good angle to use. I predict that the difference in the mass of the ball will not affect the acceleration of it. I am able to make my prediction by using my own knowledge and information from textbooks. The greater the mass of an object, the greater force needed to accelerate it. Therefore when two objects fall in a gravitational field, although the object with twice the mass has twice the gravitational force acting on it, it needs twice the force to accelerate it at the same rate as the smaller mass. For this reason ALL objects accelerate at the same rate ignoring air resistance. Prediction Using the sin function I can find out how high the ramp has to be for a 5° angle. The length of the ramp is 124.8cm. 124.8 sin 5° = 10.88cm(this is the height the ramp must go) I know that by dropping a ball straight down, at a 90° is roughly 9.8m.s.2. By dividing 9.8 by 90 and multiplying it by 5, I can effectively get the acceleration of the ball due to gravity. 9.8 / 90 = 0.108 Þ 0.108 * 5 = 0.54 The acceleration of the ball is 0.54m.s.. As stated earlier the mass of the ball does not affect the acceleration, all the accelerations should be the same. Mass of the ball / g 6.06 7.30 8.63 28.07 Predicted acceleration / m.s2 0.54 0.54 0.54 0.54 CHANGING THE ANGLE OF THE RAMP In this experiment I will keep all aspects of the experiment constant except for the angle of the ramp that the ball rolls down. For this experiment I will need to use a plastic ramp, a stand, a clamp, a nail, a metre rule, a ball bearing, four metal electrodes, four crocodile clips, four wires stopclock. The set up of the apparatus is the same as the last experiment, as shown below. The ramp will be initially set up to get a 5° angle. From the previous experiment we know that to achieve a 5ÿ angle the ramp will be set up 10.9cm off the ground. I have gone through the method for this later. The same method will be used as before. I will use the same ball which weighs 28.07g each time even though all masses should accelerate at the same rate. I do this just so that the environment is completely fixed apart from the angle of the ramp. The metal ball will be released from the top of the ramp and allowed to roll down. The ball will be rolled down twice. On the first roll, the final velocity of the ball as it rolls down the ramp will be measured. This will be measured by connecting wires to the stopclock and set points on the ramp. The electrodes are placed close together either side of the ramp. As the metal ball rolls over them, it completes the circuit and starts the stopclock. As it then rolls over the second set, it again completes the circuit and stops the clock. I will take three readings, and in the end take the average. I will then be able to work out the velocity by using the formula as shown on the next page. Distance travelled in a given direction (m) 1. Velocity (m.s1) = Time taken (s) On the second roll, the time it takes to roll from the top to the bottom will be measured. As the metal ball rolls over the electrodes at the top, it completes the circuit and starts the stopclock. As it then rolls over the second set of electrodes, it again completes the circuit and stops the clock. Again I will take three readings, and in the end take the average. I already know the initial velocity to be zero, so using the final velocity and the time it takes the ball to roll down the ramp; I can work out the acceleration of the ball. I can work this out using the formula below. Change in velocity (m.s1) 2. Acceleration (m.s2) = Time taken for the change (s) I will do this with six different angles. I will use the angles 5°, 10°, 15°, 20°, 25° and 30°. From my preliminary work, these seemed like a good range of angles to use. To make it a fair test I will need to release each ball from the same spot on the ramp. On the second roll, the time it takes to roll from the top to the bottom will be measured. As the metal ball rolls over the electrodes at the top, it completes the circuit and starts the stopclock. As it then rolls over the second set of electrodes, it again completes the circuit and stops the clock. Again I will take three readings, and in the end take the average. I already know the initial velocity to be zero, so using the final velocity and the time it takes the ball to roll down the ramp; I can work out the acceleration of the ball. I can work this out using the formula below. The further the ball falls, the faster it will go so if I release them from different heights the acceleration of the balls will be different. When I measure the times for the balls, In theory it should not matter what ball I should use as mass should not matter to the acceleration. However to make it a 'proper' fair test, I will only use one ball for all the readings. I have chosen to use a ball with a mass of 28.07g because from my preliminary work, which I carried out before the experiment, it seemed like a good weight to use. It is big enough to connect both electrodes easily, but small enough to roll properly through along the ramp. A bigger ball could catch on the crocodile clips. I predict that the closer the angle is to 90°, the faster it will accelerate. I am able to make my prediction by using my own knowledge and information from textbooks. When objects fall naturally, they fall at a 90° angle. On earth, the acceleration due to gravity acting on an object is 9.8m.s.2, when the angle decreases, so does the acceleration due to gravity. For this reason, I predict that the closer the angle is to 90° the greater the acceleration the ball will have. I have worked out using the sin function how high the ramp has to be for a 5°, 10°, 15°, 20, 25° and 30° angle. The length of the ramp is 124.8cm. 124.8 sin 5° = height (10.9cm) 124.8 sin 10° = height (21.7cm) 124.8 sin 15° = height (32.3cm) 124.8 sin 20° = height (42.7cm) 124.8 sin 25° = height (52.7cm) 124.8 sin 30° = height (62.4cm) I know that at 90° gravity is roughly 9.8m.s.2. By dividing 9.8 by 90 and multiplying it by whatever the angle is, I can effectively get the acceleration of the ball due to gravity. 9.8 / 90 = 0.108 È 0.108 * 5 = 0.54 9.8 / 90 = 0.108 È 0.108 * 10 = 1.08 9.8 / 90 = 0.108 È 0.108 * 15 = 1.62 9.8 / 90 = 0.108 È 0.108 * 20 = 2.16 9.8 / 90 = 0.108 È 0.108 * 25 = 2.70 9.8 / 90 = 0.108 È 0.108 * 30 = 3.24 The acceleration of the ball for a 5° angle is 0.54m.s. , for a 10° angle it is 1.08m.s.2 , for a 15° angle it is 1.62m.s. 2, for a 20° it is 2.16m.s. 2, for a 25° angle it is 2.70m.s.2 , and for a 30° angle it is 3.24m.s.2 . As the mass of the ball does not affect the acceleration, all the accelerations should be the same. Steepness of ramp / ° 5 10 15 20 25 30 Predicted acceleration / m.s2 0.54 1.08 1.62 2.16 2.70 3.24 RESULTS Changing the Mass of the Ball Mass of the Ball (g) 6.06 7.30 8.63 28.07 Acceleration (m.s.2) (Reading 1) 0.50 0.53 0.56 0.54 Acceleration (m.s. 2) (Reading 2) 0.52 0.52 0.55 0.53 Acceleration (m.s. 2) (Reading 3) 0.54 0.50 0.52 0.53 Average/ (m.s. 2) 0.52 0.52 0.54 0.53 Changing the Angle of the ramp The angle of the ramp (ÿ) 5.0 10.0 15.0 20.0 25.0 30.0 Acceleration (m.s. 2) (reading 1) 0.54 1.01 1.60 2.10 2.71 3.23 Acceleration (m.s. 2) (reading 2) 0.53 1.03 1.62 2.18 2.63 3.26 Acceleration (m.s.2) (reading 3) 0.53 1.12 1.64 2.19 2.70 3.23 Average (m.s. 2) 0.53 1.05 1.62 2.16 2.68 3.24 Conclusion As you can see from the graph as the angle of the ramp goes up so does the acceleration and it goes up very steadily the smallest gap between readings is 52 m.s.2 while the biggest difference between readings was 57m.s.2. These results show that when the angle of the ramp is increased the speed increases in turn whereas the acceleration between the 5ÿ intervals is roughly the same around 54m.s. 2. Between these intervals the acceleration between 5ÿ angles does not change but the speed does. I predicted these accurately by using my previous knowledge, which is that at 90ÿ, objects accelerate at 9.8m.s. 2 so by dividing the acceleration at 90ÿ by 90 you get the acceleration at 1ÿ then you can multiply that by the angle e.g. at 10ÿ you would multiply 0.108 by 10 to obtain an acceleration of 1.08m.s. 2. When the variable was the mass of the ball, the times of the accelerations were all in a range of 0.02m.s. 2. This reinforces the fact that all masses, ignoring air resistance, accelerate at the same rate. This is because the greater the mass of an object the more force it needs to accelerate it. In my prediction I was very close to the actual results, as I knew that all objects accelerated at the same rate and as I knew that at 90ÿ it accelerated at 9.8m.s2 so by dividing the acceleration at 90ÿ by 90 I could tell the acceleration at 1ÿ would be 0.108m.s.2 so by multiplying by 5 I could find out what the acceleration should be for all of the ball bearings. When the variable was the mass of the ball I had to repeat one of my readings when the ramp slipped. Evaluation I think the experiment was carried out successfully when I drew my graph I could spot no anomalous results. If I were to do this experiment again I would use a smoother ramp, the ramp that I used may have caused the ball to bobble and this would be remedied with a smoother ramp. When the variable was the mass of the ball I had to repeat one of my readings when the ramp slipped this should not have been a problem but I did not fasten the clamp enough. Future experiment improvement I could take more readings to iron out any anomalous results and get a more definite average. In a followup experiment I could see how different materials reacted in this experiment. In a further experiment I could see what affects an obstacle in the middle of the ramp would have. 
