# Conservation of Linear Momentum Abstract

Conservationof Linear Momentum

Abstract

Theaim of the experiment was to study the momentum and energyconservation for two bodies during a collision and to determine ifboth energy and momentum are conserved. The experimental designinvolved a ballistic pendulum which measured the angle of launch.With two known masses, the setup was used to measure the angle oflaunch which was used to determine the height of the two bodies afterthe collision. Newton’s Laws of motion were then used to determinethe Momentum before and after collision together with the kineticenergies. The two bodies were found to experience complete inelasticcollision since there was a loss of kinetic energy before and afterthe collision.

Momentumis the product of the mass of a small object and its velocity. Sincemomentum is determined using velocity, it is a vector quantity. Themomentum of more than one particle is achieved by factoring all thedirectional components of all the individual momenta. Thus, themomentum for several particles is the vector sum of the individualmomenta. Since each object has their own individual momentum, duringa collision, the objects interact with each other. The behavior ofobjects during collision of guided by Newton’s laws of motions. Thelaws can be applied in the analysis of collisions between objects.When two objects collide, the interaction can either be elastic orinelastic. An elastic collision is defined as the interaction of twobodies in motion such that there is no loss in kinetic energy. Aninelastic collision is where during collision, part of the kineticenergy is changed to other forms of energy.

ElasticCollison

Momentumis given as the product of mass and velocity

P=mv

WhereV is a vector quantity, M is the mass of the object

Inan elastic collision, the energy is defined as the kinetic energy.Kinetic energy described the energy from the particles that are inmotion. For an elastic system with mass A and B, the momentum beforeand after collision is seen to be equal.

Initialmomentum for A = *m**A**v**Ai*

Initialmomentum for B*= m**B**v**Bi*

Finalmomentum for A = *m**A**v**Af*

Finalmomentum for B = *m**B**v**Bf*

Fora system in elastic collision

Initialmomentum = Final Momentum

*m**A**v**Ai*+*m**B**v**Bi*=*m**A**v**Af*+*m**B**v**Bf*

Foran elastic system the kinetic energy is also conserved. Kineticenergy in an elastic system is given by

KE= 1/2MV^{2}

Fora system of collision of particles A and B

InitialKinetic Energy for A =

InitialKinetic Energy for B =

InitialKinetic Energy for A =

InitialKinetic Energy for B =

InitialKinetic Energy =Final Kinetic Energy

InelasticCollision

Elasticcollision is a type of collision which there is a loss of kineticenergy. For this system, the momentum is conserved by kinetic energyis not.

Figure1: Ballistic Pendulum

Sincemomentum is conserved before and after collision, the momentum of theproject is equal before and after collision. Mp is the Momentum ofthe particle before collision and Vp is the velocity of the particlebefore collision. VB is the velocity of the particle after collision.

*m**P**v**P*=(*m**B*+*m**P*)*v**B*

Foran inelastic system, the kinetic energy is not conserved but themechanical is conserved. According to figure 1, particleblock rises up to a maximum height *h* undera gravitational acceleration g.

Solvingthe equation MP-MB is cancelled on both sides

WhereVB is after collision

Methods/Procedure

Thependulum was set up as shown in figure 2. The masses were firstweighed and recorded. The pendulum was balanced on a ruler until thecenter of the Center of gravity was determined. The length of thependulum was also recorded. The angle pointer was then moved toadjust the contact of the pendulum arm. The angle was then recordedas Θ^{0}.The pendulum was then latched at 90 degrees and fasted. The steelball was then inserted to the middle of the maximum range position.The angle pointer was then moved to Θ­_{0}.The pendulum was then released by the cannon and the maximum heightand maximum angle from the angle indicator was recorded. Theprocedure was the repeated five times.

Results

L (m) |
0.3050 |

m |
0.0100 |

M |
0.2455 |

Trial |
Angle (Deg) |
H (m) |

1 |
8.0 |
0.0030 |

2 |
7.0 |
0.0023 |

3 |
8.0 |
0.0030 |

4 |
6.0 |
0.0017 |

5 |
4.0 |
0.0007 |

Average |
6.6 |
0.0021 |

Std. Dev. |
1.5 |
0.0009 |

DataAnalysis

Usingthe data generated from the Lab, the following were determined

Themaximum height travelled

ButL =0.3050 (from practicals) and

FinalVelocity

InitialVelocity

InitialKinetic Energy

FinalKinetic Energy

PercentageLoss in kinetic Energy after collision

Theparentage loss is given by ration of Momentum after

Discussionand conclusion

Accordingto the findings, it is established that there is a loss of kineticenergy of 96.06% after the collision. The kinetic energy was thus notconserved after the collision. A system is described as elastic ifall the Kinetic energy is conserved before a collision and after acollision. In an inelastic system, the kinetic energy is notconserved after a collision. The loss seen in the results shows thatthe system after the collision was inelastic. Despite the Kineticenergy not being conserved, the linear momentum was conserved sincethe momentum after the collision was found to be equal to momentumafter the collision. During the experiment, it was assumed that thekinetic energy would not be conserved. According to the setup, it wasalso assumed that there was no friction generated by the anglemeasuring equipment. As the ball, travels in the air, it was alsoassumed that there was no friction between the surface of the balland air. The objectives of the experiment which was to determine ifboth momentum and kinetic energy are conserved in real worldapplication. According to the results determined by the experiment,it was proved that both momentum and kinetic energy cannot beconserved. In conclusion, the objectives of the experiment were metsince it was determined that for any two objects in a collision, themomentum is conserved, but the kinetic energy is not conserved. Someof the kinetic energy is converted to heat or sound energy. Thetheoretical values are in line with the experimental values since theKinetic energy was not conserved while the momentum was conserved.

Reference

Viegas,J. (2005). *Kineticand potential energy: Understanding changes within physical systems*.New York: Rosen Pub. Group.

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