Science Inquiry
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Rishi Garg Physics, 6th Period Mr. McQueen 11 March 2008 Science Inquiry Project
Question: Are Newton's second and third laws of motion true? Hypothesis: I believe that Newton's second and third laws are true. Newton’s second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass. The formula for Newton’s second law is: F=ma, where F is force, m is mass, and a is acceleration. This means that an object’s net force is equal to the product of its mass and acceleration. Newton’s third law states that if two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction. In other words, when one object hits another, the second object moves away in a direction opposite to the first object with an equal force. I will use two carts of the same mass. This will help me because I can take one variable out of the situation. Now, the modified version of Newton’s second law formula is F=a. Also, in order to prove both laws at the same time, I can take force out of the situation. This is because, according to the modified second law formula, force is equal to acceleration. Therefore, theoretically according to Newton’s third law, when one of the carts hits the other, both of them should have the same acceleration. If they do indeed
have the same acceleration, I will have proven Newton’s second and third laws to be true.
Materials:
Two metal carts with equal mass
One metal ramp for carts
Two Vernier motion detectors
One LabPro
Two brackets for motion detectors
Two pairs of magnets for carts
Two notecards
Tape for the notecards
Computer with Logger Pro software
Variables: Independent – the acceleration of the first cart just before it hits the second cart Dependent – the acceleration of the second cart just after it gets hit by the first cart
Procedure:
Install one pair of magnets in each cart, making sure that the magnets are directed in a way that the two carts repel each other.
Set up the ramp and adjust it so that the two carts stay in place while on the ramp and do not roll because of an incline.
Tape each notecard to the end of each cart that is closest to the motion detector on each of the carts’ respective sides, in a way that blocks each detector from seeing the cart that is further away from it.
Attach the two motion detectors to the brackets.
Attach the one bracket to each end of the metal ramp and secure them so that they will not move when a cart crashes into one of them.
Connect the LabPro to the computer and to a power source.
Connect the two motion detectors to the LabPro.
Open the Logger Pro software on the computer and set it up so there are two graphs; one with time vs. acceleration 1 and the other with time vs. acceleration 2 (1 and 2 denote the two different motion detectors)
Place a cart on the ramp so that the edge of the cart is at the 60 cm line (using the scale on the ramp).
Position the second cart on the ramp so that the magnets inside it are pointed a direction that will repel the first cart. Also, place the cart at the very end of the ramp.
Have one student ready to push the "Collect" button in Logger Pro and another student ready to push the second cart toward the first cart.
Have the first student push the "Collect" button, then have the second student push the second cart somewhat slowly (does not have to be exact) toward the first cart.
After the first cart reaches the other end of the ramp, have the first student press the "Stop" button in Logger Pro.
Record the highest acceleration from each of the two graphs.
Repeat steps 8-13, each time increasing the velocity of the pushed cart.
Data: Max. Accel. 1 (m/s^2) Max. Accel. 2 (m/s^2)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
2.6
2.9
3.1
3.5
4
2.3
2.7
2.9
3.25
3.75
(Graph on next page)
Analysis: In my science inquiry project, I was trying to prove Newton’s second and third laws of motion. Newton’s second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass. The formula for Newton’s second law is: F=ma, where F is force, m is mass, and a is acceleration. This means that an object’s net force is equal to the product of its mass and acceleration. Newton’s third law states that if two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction. In other words, when one object hits another, the second object moves away in a direction opposite to the first object with an equal force. Throughout my project, I assumed that Newton’s second and third laws were true, unless proved otherwise by me. In order to prove both of these laws in using one procedure, I realized that I could use two carts with the same mass. This helped me because since the masses were equal, I could take one variable out of the situation. Now, the modified version of Newton’s second law formula is F=a. Also, in order to prove both laws at the same time, I realized that I could take force out of the situation. This is because, according to the modified second law formula, force is equal to acceleration. Therefore, theoretically according to Newton’s third law, when one of the carts hits the other, both of them should have the same acceleration. This made my project very simple because I only needed to measure one variable: acceleration. In order to properly prove these two laws, I realized that I needed to do many trials with different accelerations of the first cart in each. I decided to start with a low acceleration, then to increase it each time. It didn’t matter
exactly what the acceleration each time was; it only mattered if the first and second carts’ accelerations were the same. In the first trial, the first cart’s acceleration was 2.6 m/s2. The second cart’s acceleration was 2.3 m/s2. The difference between the two is only 0.3 m/s2. In the second trial, the first cart’s acceleration was 2.9 m/s2, and the second cart’s acceleration was 2.7 m/s2. This time, the difference was only 0.2 m/s2. In the third trial, the first cart’s acceleration was 3.1 m/s2, and the second cart’s acceleration was 2.9 m/s2. The difference is, again, 0.2 m/s2. In the fourth trial, the first cart’s acceleration was 3.5 m/s2, while the second cart’s acceleration was 3.25 m/s2. The difference in this trial was only 0.25 m/s2. In the last trial, the first cart’s acceleration was 4.0 m/s2 while the second cart’s acceleration was 3.75 m/s2. Again, the difference is only 0.25 m/s2. As one can see, the differences between the first and second carts’ accelerations are always below 0.3 m/s2. This negligible difference can be explained by analyzing the reliability and limitations of my procedure. I used Vernier motion detectors to measure the acceleration of the two carts. Although these are very useful devices, they are not completely accurate. Scientific devices can never be accurate, even though they can be very close. Also, the carts might have been slightly different from each other. For example, the axel in one of the carts might have been set a different way from the other, causing more friction in that cart and therefore reducing the overall acceleration. Another reliability issue might involve the metal ramp. Although there is very little friction and the track looks extremely smooth, there might have been slight imperfections in the track, causing the carts to lose some of their acceleration. Because of all these possible limitations, it is understandable to have a slight deficit in the data. This means that since the accelerations of the two carts were extremely similar in each trial, it is safe to say that under ideal conditions, they would have been the same. Therefore, I have successfully proven Newton’s second and third laws of motion to be true.
If I were to do this project again, I would definitely modify my procedure in order to be more accurate. First of all, I’d make sure that the two motion detectors were calibrated the same way before I began my testing. I’d probably also measure the distance the carts traveled and use that to calculate the acceleration, so that I would have the acceleration calculated from two different sources. I would then compare them and make sure that they were very similar. This would ensure accuracy of the data. If I were told to build upon this project, I would use objects with different masses to prove Newton’s second and third laws. For example, I might use a basketball and a tennis ball. I might also try proving only the third law using sound waves and a surface on which to receive the waves. I think that it would be interesting to see if the law applies to things we can’t see.
Question: Are Newton's second and third laws of motion true? Hypothesis: I believe that Newton's second and third laws are true. Newton’s second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass. The formula for Newton’s second law is: F=ma, where F is force, m is mass, and a is acceleration. This means that an object’s net force is equal to the product of its mass and acceleration. Newton’s third law states that if two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction. In other words, when one object hits another, the second object moves away in a direction opposite to the first object with an equal force. I will use two carts of the same mass. This will help me because I can take one variable out of the situation. Now, the modified version of Newton’s second law formula is F=a. Also, in order to prove both laws at the same time, I can take force out of the situation. This is because, according to the modified second law formula, force is equal to acceleration. Therefore, theoretically according to Newton’s third law, when one of the carts hits the other, both of them should have the same acceleration. If they do indeed
have the same acceleration, I will have proven Newton’s second and third laws to be true.
Materials:
Two metal carts with equal mass
One metal ramp for carts
Two Vernier motion detectors
One LabPro
Two brackets for motion detectors
Two pairs of magnets for carts
Two notecards
Tape for the notecards
Computer with Logger Pro software
Variables: Independent – the acceleration of the first cart just before it hits the second cart Dependent – the acceleration of the second cart just after it gets hit by the first cart
Procedure:
Install one pair of magnets in each cart, making sure that the magnets are directed in a way that the two carts repel each other.
Set up the ramp and adjust it so that the two carts stay in place while on the ramp and do not roll because of an incline.
Tape each notecard to the end of each cart that is closest to the motion detector on each of the carts’ respective sides, in a way that blocks each detector from seeing the cart that is further away from it.
Attach the two motion detectors to the brackets.
Attach the one bracket to each end of the metal ramp and secure them so that they will not move when a cart crashes into one of them.
Connect the LabPro to the computer and to a power source.
Connect the two motion detectors to the LabPro.
Open the Logger Pro software on the computer and set it up so there are two graphs; one with time vs. acceleration 1 and the other with time vs. acceleration 2 (1 and 2 denote the two different motion detectors)
Place a cart on the ramp so that the edge of the cart is at the 60 cm line (using the scale on the ramp).
Position the second cart on the ramp so that the magnets inside it are pointed a direction that will repel the first cart. Also, place the cart at the very end of the ramp.
Have one student ready to push the "Collect" button in Logger Pro and another student ready to push the second cart toward the first cart.
Have the first student push the "Collect" button, then have the second student push the second cart somewhat slowly (does not have to be exact) toward the first cart.
After the first cart reaches the other end of the ramp, have the first student press the "Stop" button in Logger Pro.
Record the highest acceleration from each of the two graphs.
Repeat steps 8-13, each time increasing the velocity of the pushed cart.
Data: Max. Accel. 1 (m/s^2) Max. Accel. 2 (m/s^2)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
2.6
2.9
3.1
3.5
4
2.3
2.7
2.9
3.25
3.75
(Graph on next page)
Analysis: In my science inquiry project, I was trying to prove Newton’s second and third laws of motion. Newton’s second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass. The formula for Newton’s second law is: F=ma, where F is force, m is mass, and a is acceleration. This means that an object’s net force is equal to the product of its mass and acceleration. Newton’s third law states that if two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction. In other words, when one object hits another, the second object moves away in a direction opposite to the first object with an equal force. Throughout my project, I assumed that Newton’s second and third laws were true, unless proved otherwise by me. In order to prove both of these laws in using one procedure, I realized that I could use two carts with the same mass. This helped me because since the masses were equal, I could take one variable out of the situation. Now, the modified version of Newton’s second law formula is F=a. Also, in order to prove both laws at the same time, I realized that I could take force out of the situation. This is because, according to the modified second law formula, force is equal to acceleration. Therefore, theoretically according to Newton’s third law, when one of the carts hits the other, both of them should have the same acceleration. This made my project very simple because I only needed to measure one variable: acceleration. In order to properly prove these two laws, I realized that I needed to do many trials with different accelerations of the first cart in each. I decided to start with a low acceleration, then to increase it each time. It didn’t matter
exactly what the acceleration each time was; it only mattered if the first and second carts’ accelerations were the same. In the first trial, the first cart’s acceleration was 2.6 m/s2. The second cart’s acceleration was 2.3 m/s2. The difference between the two is only 0.3 m/s2. In the second trial, the first cart’s acceleration was 2.9 m/s2, and the second cart’s acceleration was 2.7 m/s2. This time, the difference was only 0.2 m/s2. In the third trial, the first cart’s acceleration was 3.1 m/s2, and the second cart’s acceleration was 2.9 m/s2. The difference is, again, 0.2 m/s2. In the fourth trial, the first cart’s acceleration was 3.5 m/s2, while the second cart’s acceleration was 3.25 m/s2. The difference in this trial was only 0.25 m/s2. In the last trial, the first cart’s acceleration was 4.0 m/s2 while the second cart’s acceleration was 3.75 m/s2. Again, the difference is only 0.25 m/s2. As one can see, the differences between the first and second carts’ accelerations are always below 0.3 m/s2. This negligible difference can be explained by analyzing the reliability and limitations of my procedure. I used Vernier motion detectors to measure the acceleration of the two carts. Although these are very useful devices, they are not completely accurate. Scientific devices can never be accurate, even though they can be very close. Also, the carts might have been slightly different from each other. For example, the axel in one of the carts might have been set a different way from the other, causing more friction in that cart and therefore reducing the overall acceleration. Another reliability issue might involve the metal ramp. Although there is very little friction and the track looks extremely smooth, there might have been slight imperfections in the track, causing the carts to lose some of their acceleration. Because of all these possible limitations, it is understandable to have a slight deficit in the data. This means that since the accelerations of the two carts were extremely similar in each trial, it is safe to say that under ideal conditions, they would have been the same. Therefore, I have successfully proven Newton’s second and third laws of motion to be true.
If I were to do this project again, I would definitely modify my procedure in order to be more accurate. First of all, I’d make sure that the two motion detectors were calibrated the same way before I began my testing. I’d probably also measure the distance the carts traveled and use that to calculate the acceleration, so that I would have the acceleration calculated from two different sources. I would then compare them and make sure that they were very similar. This would ensure accuracy of the data. If I were told to build upon this project, I would use objects with different masses to prove Newton’s second and third laws. For example, I might use a basketball and a tennis ball. I might also try proving only the third law using sound waves and a surface on which to receive the waves. I think that it would be interesting to see if the law applies to things we can’t see.
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