As seen in the previous section, in a collision, two objects that start off separate bump into each other. Momentum is always conserved, but at the same is not found to be true for energy. In some collisions, kinetic energy is conserved; but in most collisions energy is lost in the form of sound, heat, or damage to one or more of the objects.
Collisions where energy is lost are called inelastic, and they fall into the following two categories:
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Inelastic collisions Inelastic collisions occur when two objects bump into each other and then move off separately. They are described by the following equation: m1v1i + m2v2i = m1v1f + m2 v2f Notice that both sides of the equation describe the momentum of two separate objects. |
Perfectly inelastic collisions Perfectly inelastic collisions occur when two objects bump into each other and then stay connected. They are described by the following equation: m1v1i + m2v2i = (m1 + m2) vf In this equation, the left side describes two separate objects, but the right side describes only one object (with both masses combined and one final velocity). |
In the following simulation, you can change the masses of both carts and the starting velocity of cart A. You can also decide the type of equation by setting the value of e. If e is a decimal between 0 and 1, it is inelastic. If e = 0, then the collision will be perfectly inelastic.
In the simulation, use the following variables:
| simulation | mA | mb | uA | uB | VA | VB |
| this lesson | m1 | m2 | v1i | v2i | v1f | v2f |
Copy the following chart, and then run the collisions in the animation and record the values. Plug the mA, mB, uA, uB, vA, and vB into the collision equation, and in the table record the values of both the right and left sides of the equation to check if they are equal.
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e
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mA
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mB
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uA
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uB
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vA
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VB
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Right side
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Left side
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.5
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1
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1
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2
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0
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.5
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3
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2
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2
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0
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.5
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5
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3
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2
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0
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0
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1
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1
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2
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0
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0
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3
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2
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2
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0
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0
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5
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3
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2
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0
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| e | mA | mB | uA | uB | vA | VB | Right side | Left side |
| .5 | 1 | 1 | 2 | 0 | .5 | 1.5 | 2 | 2 |
| .5 | 3 | 2 | 2 | 0 | .8 | 1.8 | 6 | 6 |
| .5 | 5 | 3 | 2 | 0 | 1.875 | 1.875 | 10 | 10 |
| 0 | 1 | 1 | 2 | 0 | 1 | 1 | 2 | 2 |
| 0 | 3 | 2 | 2 | 0 | 1.2 | 1.2 | 6 | 6 |
| 0 | 5 | 3 | 2 | 0 | 1.25 | 1.25 | 10 | 10 |
If two objects start out together and then push off from one another, or if one object breaks into two pieces that move apart; physicists call this an explosion. This is like a perfectly inelastic collision in reverse. The equation looks very similar to the following:
(m1 + m2) vi = m1v1f + m2 v2f
The classic physics example is two students standing together on roller skates push off from one another. If the 60 kg student moves to the left at 3 m/s, how fast will the 90 kg student be moving?
Given: m1 = 60 kg m2 = 90 kg vi = 0 m/s v1f = -3 m/s (left = negative)
Unknown: v2f = ?
Equation: (m1 + m2)vi = miv1f + m2v2f
Simplify: vi = 0 m/s, so the equation becomes: 0 = m1v1f + m2v2f or -m1v1f = m2v2f
Solve: -m1v1f = m2v2f
-(60)(-3) = 90v2f
180 = 90v2f
2 = v2f
v2f = 2 m/s
What does an avalanche have to do with the conservation laws?
Watch the video below of an avalanche in action to find out.
Source: Everest Massive Avalanche, Discovery.com, How Stuff Works
What does an avalanche have to do with the law of conservation of energy?
What does an avalanche have to do with the law of conservation of momentum?