Day 14 Notes

Friday, June 27, 1997

Chapter 6 contd. - Conservation of Momentum and Collisions.

Last time, we introduced the notion of impulse - a force times time. We talked about momentum, a state variable of motion. Today, we see the relationship between the two. We also talk about some types of collisions.

Impulse and momentum are closely related. If we look at the good old kinematics equation:

v = v₀ + at
and we multiply everything by mass, m, we see some of our new concepts appear:
p = p₀ + Ft, or Impulse = (Delta)p
In words, impulse equals change in momentum.

If we define a system (that is, a group of objects whose collective motion interests us) on which no external forces act (that is, no forces applied by objects outside the system onto objects in the system), then there is no impulse being applied to the system and thus its momentum must not change. This is called Conservation of Momentum and its condition is that No Net External Forces Act on the System.

One particularly interesting case in which momentum is conserved is a collision. A Collision is an occurence is which two or more bodies come into contact free from any net external forces. Note that a ball hitting a wall is not generally considered a collision by this definition because the wall is "nailed down" to the ground - that is, there is a net external force affecting the ball-wall system. On the other hand, two tennis balls hitting in mid-air would be a collision because of two things: (1) the external force of gravity is affecting both balls in the same way (pulling down), and (2) during the very brief time of the collision, gravity imparts very little impulse to the system, so any change in momentum is negligible anyway.

Specifically, we said that an elastic collision is one in which two objects collide and immediately come out of contact. An inelastic collision is one in which the colliding objects stick together, even if they later come apart after sticking together. In either case, momentum is conserved. In an elastic collision, kinetic energy is also conserved. Today we do some example problems involving collisions.

Did several example problems involving elastic and inelastic collisions. I will not reproduce them here.

We did not talk about 2-dimensional collisions in class. Just a few words about them: (I will not make you do any calculations with them, but it is nice to see the concept - it ties together well with several other things we have done.).

Conservation of momentum still holds for 2-d collisions. However, now your momentum vectors should be broken down into components. The x-component of momentum is conserved AND the y- component of momentum is conserved (they are conserved individually - like when we broke forces into components and used Newton's 2nd Law of Motion on the components individually). In other words, there will be two conservation of momentum equations.
Conservation of kinetic energy holds for elastic collisions. Since kinetic energy depends on speed rather than velocity, there is still only one equation for conservation of the kinetic energy - here v is NOT broken into components.

Self-Quiz

Take the quiz and see how you do...

Quiz for day number: Please don't change this!

A moving particle collides with a stationary particle and the two stick together (forever). If the moving particle does not hit the target particle head-on, the two particles will move off at some non-zero angle to the direction of the incident particle's motion...
Sometimes
Always
Never
In an elastic collision between two identical billiard balls, one of which is initially at rest, the incident ball leaves the collision at an angle of 90 degrees to the direction of its initial motion. What is the direction of motion of the target ball after the collision (relative to the initial direction of the moving ball)?
90 degrees the other way.
Same direction as the moving ball's original direction of motion.
It could fall within a wide range of possible angles.
This is an impossible situation.
A moving object of mass m collides elastically with another object (initially at rest) and rebounds straight backward at half of its original speed. What is the mass of the other object?
m
2m
3m
Need more information
Two identical particles approach each other head-on at equal speeds. If the particles undergo an elastic collision, then after the collision:
Both particles will be at rest.
One particle will be at rest and the other will move backward at twice its original speed.
Both particles will rebound straight backward with equal speed, but that speed can have any value.
Both particles will rebound straight backward with equal speed, and that speed will equal the original speed of of the particles.
No way to tell

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Attempt number: 1 2 3 4 5

Last modified 05 July 1997
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