Collisions

SECOND EDIT BY SUNGJAE HYUN IN 2016-04-16 ADDITIONS MADE BY (currently in progress, adding computational model and difficult problem) Sam Webster 4-17-16

This topic covers Collisions, a comprehensive way to combine the Momentum and Energy Principles.

The Main Idea

Collisions are special types of contact interactions between objects. From a physics standpoint, collisions are a way to combine the Momentum and Energy Principles. In the case of collisions, if we choose a system of the two objects interacting, the change in momentum of the system and the change in energy of the system are both zero. With this in mind, calculations with collisions become very simple. There are two types of collisions, Elastic Collisions and Inelastic Collisions.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript [File: CollisionsExample.py]

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Example 1) A 0.5 kg soccer ball is moving with a speed of 5 m/s directly toward to 0.7 kg basket ball which is at rest. When two balls collide and sticks together what will their final velocity be?

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m1 = 0.5 kg v1,init = 5 m/s m2 = 0.7 kg v2,init = 0 m/s

So m1 * v1 + m2 * + v2 = (m1 + m2) * vfinal

LHS = 0.5 * 5 + 0.7 * 0 = 2.5 kg*m/s RHS = (0.5 + 0.7) * vfinal = 1.2 * vfinal

LHS = RHS in inelastic collision

2.5 = 1.2 * vfinal

vfinal = 2.5 / 1.2 = 2.08333

Thus, the final velocity is 2.08 m/s.

Middling

Example 2) A bullet of 50 caliber machine gun is 42 grams. It strikes a wooden target block of mass 10 kg stationed on a friction-less surface. The wooden block gains velocity of 1.8 m/s after being embedded with the bullet. What was the velocity of the bullet before it collided with the target?

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m1 = 42/1000 = 0.042 kg v1,init = ? m2 = 10 kg v2,init = 0 m1,2 = 0.042kg + 10kg vfinal = 1.8 m/s

m1 * v1,init + m2 * v2,init = (m1 + m2) * vfinal

0.042 kg * v1,init = (0.042 + 10) * 1.8 m/s v1,init = 18.0756 / 0.042 = 430.37 m/s

Final Answer: The bullet's speed is 430.37 m/s.

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