Collisions in One Dimension LAb Report

Collisions in One Dimension

Mahmoud Mirza TA: Joseph Shammas 10/28/12

Abstract: The purpose of this lab is to study the conservation of energy and linear momentum in both elastic and perfectly inelastic one-dimensional collision. To fo that we will use two cars on a straight track. We will have two sensors to collect the data. At different parts we will flip around the carts and make use the magnet so as to make the carts become one body. The velocities measured in these experiments after the collision will be compared with the corresponding theoretical predictions.

Objective: In this lab we are going to show that momentum is always conserved when there is no net external force acting on the system and that energy is only sometimes conserved in different kinds of collisions. This is a simple way to understand more complex situations such as a real car accident or any complex collision we see in reality. The linear momentum conservation is one of the more important theories when it comes to the discoveries of Newton. It was called “Theorem of Linear Momentum Conservation”. For a single particle of mass m and velocity v, the linear momentum is defined as p = m v. In this case both are vectors since direction should be recorded. For a system of n masses m1, m2…mn with velocities v1, v2, vn, the linear momentum of the system is defined as p of a certain system = p1 + p2 +… + pn = m1 v1 + m2 v2 +… + mn vn. The Theorem of Linear Momentum Conservation states, “if the sum of all forces acting on a system of particles is zero, then P of the system is considered to be conserved. In this specific lab we will test this using two carts while we keep initial and final data recorded. Furthermore, what we are trying to reach is P(system) before the collision and P system after the collision equal each other. Of course when we take account of some friction and air resistance we will not get perfect results; however, we should be close. The kinetic energy of a body id defined as KE= ½ m v2. Yet, when we measure KE for a system we use KEsys=KE1+KE2+..KEn=1/2m1v12_1/2m2v22.  As for for the Velocity equations for elastic and inelastic collisions between two gliders. We use the following equations: 1. vf = m1 v1i/ (m1 + m2) for perfectly inelastic collisions 2. v1f = (m1 – m2) v1i/ (m1 + m2) for elastic 3. v2f = 2 m1 v1i/ (m1 + m2) elastic Procedure: Photo gates will have the purpose of recoding the position as a function of time. We start the experiment by measuring the two carts and recording all data. Then we specify the carts in the system by the software. In excel you will prepare a data table. Make a segment for all five experiments. Then there will be a list of what variable speed to be present in the data such as what velocities to take before and after. Then you will calculate momentum and energy. There will be three parts in the procedure section that will lead you through collecting data and typing it in exel. Data Analysis Will be attached at the end of the lab. Set up maybe a little different since I attended another lab that week. Discussion: 1.the ratio of the speeds was close to the theoretical value of 1. Is it a little off due to minor errors such as friction and our hands. It is not possible that we get the same exact push. Furthermore, the track itself could not be perfect either. So small errors like these push you in small values away from the theoretical value. A way to correct this data is to use a spring to ignite our carts for example. Also, another way is to clean the track with something that decreases friction as much as possible. We

allow the values to be less that 10% and KE to be less than 20% because there are factors that cause the data to shift from theoretical values. Theoretical values are set in a way where all variables are held constant and this is only possible is a perfect scenario. The human hand, friction, air resistance, and other factors will affect the results and we use these percentages as a approximation to disregard these. Conclusion: The objective was met since the values were close to theoretical values. Meaning, the data is correct however the aspect talked about above like friction and air resistance will throw us a little off. In collision 4 and 5 the energy is conserved since the chance between the runs was minor. The results of the fractional change recorded in the data does agree with the theory since it was not greater than the approximated percentages.