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Explosions and Collisions

An explosion results when internal parts of an object—or a system (collection) of objects interact in ways that separate the parts. But if we analyze the total momentum of all the resulting parts, that total is exactly the same as the total momentum of the original object(s).So long as the transactions were all internal (“within the room”), there’s no change in the overall total vector sum of momentum:

P = Pf – Pi = 0 In other words: Pi = Pf

That is: Pi.x = Pf.x and Pi.y = Pf.y Collisions result from two or more objects coming together —sometimes staying together, sometimes not. But again, if all the transactions happen “within the room” (the space whose borders are not crossed by other transactions with the outside), then again, there is no change in the system’s overall momentum, P.

Two ice skaters, with masses of 50 kg and 75 kg are at the center of a 60-meter diameter circular ice rink.

The skaters then push off against each other and glide to opposite edges of the rink. If the more massive skater reaches the edge in 20 sec, how long does the less massive skater take to reach the edge?

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Football player A (100 kg) is moving at 4.5 m/s when he collides and hangs onto player B (150 kg), who is moving at –2.0 m/s. Assuming the collision happens in the air (that is, the ground doesn’t influence it), describe the motion of the two players just afterward.

1. vA = 0.6 m/s vB = 0.6 m/s

2. vA = –0.6 m/s vB = 0.6 m/s

3. vA = 3.0 m/s vB = 3.0 m/s

4. vA = –4.5 m/s vB = 2.0 m/s

5. None of the above.

Problem 9.49: Two 500 g blocks of wood are 2 m apart on a frictionless table. A 10 g bullet is fired at 400 m/s toward the blocks. It passes all the way through the first block, then embeds itself in the second block. The speed of the first block immediately afterward is 6 m/s. What is the speed of the second block after the bullet embeds in it?

KEY: Determine what you will use as the ‘system’ and what your ‘initial’ and ‘final’ points are.

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Example:

Three equal mass lumps of clay flying through the air horizontally hit each other and stick together.

The original velocity of one lump was 4 m/s in a direction 450 south of east. Another was 3 m/s directly west; the third lump was moving 2 m/s directly north.

What is the velocity of the combined lump immediately after the collision?

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Stone A (2 kg) is sliding due east at 6.0 m/s across frictionless ice when it collides with stone B (3 kg), which is sliding due north at 3.0 m/s. The stones do not stick together. Immediately after the collision, stone A has a speed of zero. The speed of stone B is then:

1. 2.0 m/s.

2. 3.0 m/s.

3. 4.0 m/s.

4. 5.0 m/s.

5. None of the above.

(Follow-up: In what direction is stone B moving?)