Conservation of Linear Momentum and Energy - Lab Report Example

Conservation of Linear momentum and Energy Introduction and theory The main objective of the experiment was to show thatmomentum is normally conserved in cases where there is no net external force that is acting on the system as well as to show that in other cases energy is conserved in different kinds of collisions. Such principles are critical in studying planetary motion, automobile collisions and subatomic particles collisions. Collisions are considered to be the best ways to study how objects interact. There has been development of conservation laws that enable us to say a little bit about what is taking place without the specific interaction details during collision. Momentum is considered to be the product of velocity and mass, hence it is expressed as kg m/sec P=m*v…….1 It is as well known to be a vector quantity and its direction is same as the velocity. There is no special name for momentum unit but commonly letter p is used to represent the momentum vector. Momentum conservation can be derived using Newton’s third law. There is conservation of momentum in cases where there is interaction of interacting objects with each other. For instance, if p1is the systems initial momentum before collision and pf is the final systems momentum after collision, then we have: ^p = (pf – pi) = 0 , ……. 2 Where pi = p1i + p2i and pf = p1f + p2f if there is collision of two carts Energy conservation is considered to be another important conservation law. Energy is not a vector but a scalar. Whereby a scalar has no direction but it has magnitude only. There is conservation of energy based on whether the forces between are conservative. Gravity magnetic forces and electric are example of conservative forces. Other forces at nuclear physics level are also conservative. Friction is considered to be the most critical non-conservative force and it was been considered in this experiment. It is non-conservative force because there is energy conversion to heat. Two bodies sticking together after collision is also considered to be another non-conservative force. This is a special friction case since the energy is converted to heat in the process The experiment dealt with collisions only in one dimension. The bodies’ motion was constrained by a horizontal track. This implied that momentum and velocity was only in one direction(x or -x).Where x represents the tracks co-ordinates. Because we dealt with 2 bodies, the momentum conservation law can be illustrated as. ………………………3 …………………………….. 4 Hence, the masses of the 2 bodies as well as their vectors velocity after and before collision is supposed to be known is order to show momentum conservation. It is mandatory to evaluate the energy after and before collision in order to find out if the energy conserved. The gravitational potential energy is not changed in this case since the motion occurs on the level surface. Energy conservation can be expressed as below; ………………….4 There is a question mark at the equal sign because there is no energy conservation In cases where a collision results to total kinetic energy before collision(KE i) being same to the total kinetic energy after collision (K E i) is referred to as elastic ………………………………………5 In cases where the total kinetic energy after collision is not same as the total kinetic energy before collision, it is referred to as inelastic. On the other hand, in cases where the objects stick together after collision, it is referred to as perfectly inelastic Procedure The two photo gates recorded the carts position as a time function. This was carried out with fences that had known band spacing. The setup of the experiment was as shown in figure 1 below Figure 1.Experiment set up Collision 1: Elastic Collision (carts of approximately equal masses) The additional mass was removed from cart 2. The carts were set up on the track with magnet bumpers that faced each other. A collision was made with m1 incident on m2 at a given speed, and in this case,m2 approaching from the other side(left).Linear fit was applied to the position vs time graphs in order to get the carts’ velocities after and before collision. Since the track and the carts were not frictionless, only a small part of the recorded position that was closest to the collision instant was fit. The above steps were repeated 3 times Collision 2: Elastic collision (carts remained separate after collision) The heavy rectangular block was added to the 2nd cart,m2=M. M1 collision was made on the stationary M, in this case with m approaching for the other direction (left).Linear fit was applied to the position vs time graphs to determine the carts’ velocities after and before collision. Since the track and the carts are not frictionless, only a small part of the recorded position that was closest to the collision instant was fit. Collision 3: Perfect inelastic collision (carts of approximately same masses stick together after collision) The masses of both carts were measured. The carts were then set with Velcro ends that faced each other. M1 collision was made on the stationary M, in this case with m approaching for the other direction (left).Linear fit was applied to the position vs time graphs to determine the carts’ velocities after and before collision. Since the track and the carts are not frictionless, only a small part of the recorded position that was closest to the collision instant was fit. Collision 4: perfectly inelastic collision (where m1 ≠ m2 and v2i=0.) A heavy block 250g was added on the 2nd cart, m2=M. The carts were set on the truck. The carts were then set with Velcro ends that faced each other. M1 collision was made on the stationary M, in this case with m approaching for the other direction (left).Linear fit was applied to the position vs time graphs to determine the carts’ velocities after and before collision. Since the track and the carts are not frictionless, only a small part of the recorded position that was closest to the collision instant was fit. Results 1) Gate: 275+- 3.6x10-4 Blue cart: 259+-1.2x10-4 =1.06 2) Gate: 322+-3.3x10-4 Blue cart: 308+-3.7x10-4 =1.045 3) Gate:0.94+- 0.0012 Blue cart: 0.927+-0.0012 =0.94/0.927 =1.01 Table1. The velocities before and after collision Perfect inelastic collision Blue V0 Blue Vf Red V0 Red Vf 0 0.420 0.842 0.414 0 0.460 0.926 0.456 0 0.581 1.17 0.579 Mass added(250g) 0 0.295 0.88 0.281 0 0.312 0.922 0.302 0 0.3 0.610 0.29 Elastic collision 0 0.474 0.666 0 0 0.649 0.538 0 0 0.867 0.752 0 Mass added(250g) 0 0.437 0.635 0.204 0 0.39 0.567 0.176 0 0.446 0.651 0.207 According to the results, the ratio of the gate to cart is equal to one. The velocities of objects with different masses after collision was different from the velocities before collisions(table 1).On the other hand, velocities for objects with equal masses was similar after and before collision Discussion The main objective of the experiment was to show that momentum is normally conserved in cases where there is no net external force that is acting on the system as well as to show that in other cases energy is conserved in different kinds of collisions. Basing on the results, the objective was met. For instance, for objects that had equal masses, there velocities before collision were almost the same as the velocities after collision. On the other hand, for objects with different masses, the velocities before collision and after collision seemed to be different. This demonstrated the fact that momentum is normally conserved in cases where there is no net external force that is acting on the system as well as energy is conserved in different kinds of collisions. References Penrose, R. J. Math. Phys. (1967) 8, 345. Penrose, R. Int. Jl Theor. Phys. (1968) 1, 61. Read More