Experiment: One-Dimensional Collisions Phys 215, T3 PDF

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my lab report for this lab - I earned an A in the lab. includes my theory, procedure, results, and conclusions, including sources of error ...

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- Experiment: One-Dimensional Collisions - 9/25/2018 - PHYS 215, T 3pm

Purpose The purpose of this experiment was to observe conservation of momentum while performing two types of one-dimensional collisions, inelastic and elastic. Both the inital and final velocities were measured in order to calculate the momentum and the kinetic energy for both the initial and final measurements.

Theory Momentum is a value that depends on an object’s mass and velocity. Changing the momentum of any object requires the application of a force, which is how Newton stated his second law of motion. The units for momentum are kg m/s. The linear momentum of an object of mass (m), moving with a velocity (v), is the product of its mass and velocity with the equation: Momentum:

A change in momentum requires the application of a force. This concept is explained by Newton’s Second Law of Motion (assuming constant mass and forces). In this experiment, we will assume that our mass is constant. If the net external force on an object equals zero, then the object’s momentum does not change. Therefore, momentum would be conserved. This can be shown by the following equation: Conservation of Momentum:

If a constant forces is acting on the object, changing its momentum, then an impulse is delivered to the object. The impulse of the force acting on an object equals the change in momentum of that object. This is called the Impulse Momentum Theorem. Impulse can be defined as:

Impulse: If two objects are interacting with each other and there are no external forces present, then the loss of momentum in one body will equal the gain in momentum of the other body. Therefore, the total change in momentum of the two bodies is zero. In other words, the Law of Conservation of Linear Momentum states “if no external force acts on a system of particles, the total linear momentum of the system cannot change.” This can be expressed as:

We have established that momentum is conserved in an isolated system (with net external forces equal to zero), but we will now consider the total kinetic energy involved in different types of collisions. The two types of collisions that we observed in these experiments were inelastic and elastic collisions. An elastic collision has two bodies that collide and then move away from each other after the collision. They do not stick together. Therefore, the objects’ shapes don’t change, and in this type of collison, both kinetic energy and momentum are conserved. In an elastic collison, the ratio of final momentum to initial momentum should be equal to 1, and the ratio of final kinetic energy to the inital kinetic energy should also be equal to 1. GAV for each will be 1. This is because both momentum and kinetic energy are conserved. Equations for these statements are shown below:

An inelastic collision is a collision in which the objects’ shape is deformed or they stick together. In an inelastic collision, the momentum is conserved, but the kinetic energy is not. Thus, in an inelastic

collision, the ratio of the final momentum to the inial momentum should be 1 (conservation of momentum, GAV = 1), but the ratio of final kinetic energy to initial kinetic energy will be less than 1. This is because some of the kinetic energy will be converted to other forms, such as sound energy or work needed to deform the objects. Equations for these statements are shown below:

Kinetic energy:

Procedure Before starting the experiment, we leveled the air track and set up Capstone on the computer as the protocol indicated. Capstone was used to measure the velocity of the carts at each of the photogates. We added a 50g mass to one of the carts in order to make it serve as the heavier cart. The mass of each cart (with the 10cm tab included) was measured with a triple beam balance. I was responsible for this part. We placed the lighter cart on the outside of one of the photgates and the heavier cart in between the two photogates. The first part of the experiment included the elastic collisions. To ensure elasticity, we set up the directionality of the carts so that the metal “bumper” sides of the carts were facing each other. Each of the carts had a 10cm tab. Someone pushed the lighter cart through the 1st photogate into the heavier cart (which was at rest (initial velocity = 0 m/s) and located between the two photogates), and the heavier cart then went through the 2nd photogate while the lighter cart went back through the 1st photogate. Someone

else was in charge of clicking Record and Stop on the computer program, and another group member watched the initial velocity as the lighter cart passed through the 1st photogate the first time. It was my job to catch the heavier cart after it passed through the 2nd photogate in order to ensure that it did not bounce back through the photogate for a second time. I also reset the heavier cart back to its resting position after each trial. We ran a total of 5 trials of the elastic collisions. Each time we recorded the inital and final velocities for the lighter cart as well as the final velocity for the heavier cart. The second part of the experiment included the inelastic collisions. The heavy cart was placed in between the two photogates (at rest, initial velocity = 0 m/s), and we removed the 10cm tab from the heavy cart. We had to measure the mass of the heavier cart without the tab using a triple beam balance. It was my job to do so. For these trials, we rearranged the directionality of the carts so that the velcro sides were facing each other. Someone gently pushed the lighter cart into the heavier cart as before. We recorded the initial velocity of the lighter cart as it passed through the 1st photogate. Representing an inelastic collision, the lighter and heavier carts stuck together due to the velcro, and the final velocity of the joined carts passing through the 2nd photogate was recorded. I was responsible for catching the joined carts as they passed through the 2nd photogate and resetting the carts for the subsequent trials. We ran 5 total trials here, too. Below are the instruments used in lab to obtain our measurements and run our trials.

Data (attached)

Analysis (attached) Diagrams:

Conclusion Our first part of the experiment (elastic collisions) yielded somewhat accurate results, with a rather low percent error (11%) when we compared our average momentum ratio of final momentum to initial momentum (1.11) to the GAV of 1 (percent error = indication of accuracy). We also compared the average for kinetic energy ratio of final kinetic energy to initial kinetic energy (1.16) to the GAV of 1 and calculated a 16% yield here, also indicating somewhat accurate results. The values obtained in lab should not have been greater than one, as energy and momentum can not be created or destroyed. Therefore, errors (listed below) interfered with our experiments. For the second part of the experiment (inelastic collisons), the results were less accurate. The mean momentum ratio of final to initial momentum was 1.238, which gives a 23.8% error. Some sources of error for both of these experiments may have been that the mass of the air cart was measured improperly, the air track could have not been levelled perfectly, and there could have been scratches on the air track leading to friction and slower movement of the cart (loss of energy there). Also, it is possible that the computer person pressed the Start button after the cart actually passed the first photogate, or likewise, the Stop button before the cart passed the 2nd photogate or 1st photogate for the second time.

For the second experiment, it is also possible that the velcro did not fully stick when the two carts collided, leading to an error in the inelasticity of the collision....