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Momentum and Collisions

# Momentum and Collisions - PHY 221 Lab#1 Introduction to...

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PHY 221 Lab 8 Momentum and Collisions Leader: Critic: Scribe: Goals : Momentum ( p =m v for a single particle of mass m and velocity v ) is a useful concept in physics. The most important reason that it is useful is that total momentum of any isolated object or system is conserved (that is to say, it does not change). The only way to change the value of the momentum is to act on the object or system with an outside force. (Newton°s 2 nd Law F =m a can also be written F =d p /dt , from F =0 it follows p =const ) Conserved quantities usually make it easier to solve some classes of physics problems. In this lab, you°ll explore collisions, where thinking about momentum and its conservation are the key to understanding what goes on. Materials: Aluminum Track Two carts with magnets Two carts without magnets but with springs Two rectangular weights Weight set (no PC data acquisition needed for this lab) Activity: 1. Elastic Collisions Collision is a process in which two objects interact with each other for a limited amount of time. In the collision process we are usually interested in relating kinematical quantities of the objects after the interaction to the kinematical quantities before the interaction. Therefore, we are not really interested how the interactions evolved over time. We just concentrate on the initial (°before°) and the final (°after°) state of the system. This makes application of conservation laws particularly suitable for collision processes. The conservation laws don°t tell us how things are evolving over time. They just let us relate kinematical quantities of an isolated system at two different instances of time. Our system will consist of two carts resting on a horizontal aluminum track. The two forces, which are external to our system, gravity and normal forces exerted on the carts by the track, cancel each other (we will neglect frictional forces). Therefore, the total momentum of the two carts is conserved p = p 1 + p 2 = m 1 v 1 + m 2 v 2 = const This is true for any collisions. Elastic collisions, by definition, are those in which total kinetic energy is also conserved. K = K 1 + K 2 = m 1 v 1 2 /2 + m 2 v 2 2 /2 = const Applying these conservation laws to the collision process we have: p i =p f K i =K f or m 1 v 1 i + m 2 v 2 i = m 1 v 1 f + m 2 v 2 f m 1 v 1 i 2 /2 + m 2 v 2 i 2 /2 = m 1 v 1 f 2 /2 + m 2 v 2 f 2 /2 Since we can control initial kinematical quantities, v 1 i , v 2 i , we can consider them as given. Final velocities are unknown. Solving this system of two equations for two unknowns, v 1 f , v 2 f , we get 2 1 2 1 2 1 1 2 1 2 2 f i i m m m v v v m m m m Page 1 of 9 PHY 221 Lab #1: Introduction to Measurements 12/28/2009 http://physics.syr.edu/courses/PHY221.07Spring/manuals/momentum-and-collisions ....

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°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°° We left the second equation blank by purpose. Since there is a full symmetry between the objects °1° and °2° in all our equations, you should be able to
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