How to deal with collisions

Two objects smash into each other. What happens afterwards? And how do you figure it out?

That's a very general description. The method of attack will depend on the details of the situation. General rules to keep in mind are:

• momentum is always conserved in the absence of external forces
• momentum is a vector, so initial Px equals final Px, initial Py equals final Py, etc.
• kinetic energy is sometimes conserved; we use the word "elastic" if KE is the same before and afterwards, and the word "inelastic" if it changes
• kinetic energy is a scalar, so initial KE equals final KE with no directions

Let's do some examples.

Football players Alex, mA = 100 kg and vA = 5.6 m/s, and Bob, mB = 89 kg, vB = 6.2 m/s collide in mid-air at the peak of their leaps. Bob grabs Alex and prepares to wrestle him to the ground.

1. Is this collision elastic or inelastic?
2. Is energy conserved?
3. Is momentum conserved?
4. What will the velocity of the two players combined be immediately after they collide in mid-air?
5. If they are at a height of h = 30 cm when they meet, how far will they move and in which direction before they hit the ground?
6. Will it be a touchdown?

A block of mass M = 4 kg slides at speed v = 5 m/s across a frictionless floor. It collides with a motionless pendulum of length L = 1 m and mass m = 10 kg. The block goes sliding backwards at speed w while the pendulum swings up to a maximum angle theta. The collision is elastic.

It's an easy problem if you know the speed w

1. Is energy conserved?
2. Is momentum conserved?
3. What is the speed of the block immediately after the collision?
4. What is the speed of the pendulum's ball immediately after the collision?
5. What is the angle theta?

A puck of mass mA = 1 kg slides at speed w = 10 m/s across a frictionless floor. It collides with a motionless puck of mass mB = 0.8 kg. After the collision, puck A moves with speed vA = 5 m/s at angle theta_A = 15 degrees to the original direction, and puck B moves with speed vB at angle theta_B to the original direction.

1. Is momentum conserved?
2. What is the horizontal velocity of puck B after the collision?
3. What is the vertical velocity of puck B after the collision?
4. What is the total speed of puck B after the collision?
5. Is energy conserved?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.