Collisions

Question 1

Physics behind collisions

Answer 1

Conservation of momentum (p) - total momentum in any direction remains constant unless acted on by an external force: m1v1 = m2v2

So momentum of each object = mv

After collision, if no external forces are applied (i.e. momentum remains constant), the total momentum = p1 + p2

Final velocity = P total / m total

Question 2

Elasticity

Answer 2

in collisions, most bodies compress slightly and often return to original shape. Some compression and restitution occurs impact: this is called elasticity (not compliance)

Question 3

Coefficient of restitution (e)

Answer 3

Tendencey for objects to return to their original shape (e)

Cant be calculated, but experiments help predict

Question 4

Newtons law of impact

Answer 4

If two bodies move toward each other along the same straight line, the difference between their velocities immediately after impact bears a constant relationship to the difference between their velocities at the moment of impact.

Therefore; Vf1 - Vf2 = -e (Vi1 - Vi2)
or -e = (Vf1 - Vf2) / (Vi1 - Vi2)

e can be thought of as a measure of energy retention

Question 5

Can estimate e for collisions using newtons laws

Answer 5

Since the velocity of a dropped object is proportional to the height from which it is dropped (and to which it rebounds)

Question 6

For bounce-type collisions, two major factors affect e

Answer 6

1) Temperature - increases in temperature increase e.

Example; hotter squash ball, hotter baseball, warmer synthetic running track.

2) Impact velocity - increases in velocity decrease e.

Example; increases in ball velocity in tennis, baseball, cricket, hockey etc. increase speed of ball after being hit.

Question 7

If two moving surfaces, six variables shown to affect impact (e.g. ball and bat, remember: m1v1 = m2v2)

Answer 7

1. Increase mass of bat (increase forward momentum: m1)
2. Increase velocity of bat (increase velocity and forward momentum of bat: v1)
3. Decrease mass of ball (lighter object has faster change of direction after collision: m2)
4. Increase velocity of ball (increase momentum of system: v2)
5. Increase angle of incidence (maintain velocity of ball, less loss of energy in collision)
6. Increase coefficient of restitution (e.g. change temperature of objects, composition of bats and balls, etc.)

Question 8

Where do we use this info?

Answer 8

Properties of surfaces (e.g. court and track surfaces, balls, bats, rackets, shoe soles, pucks, etc.)

Manipulation of impacts for energy absorption (e.g. protective equipment for soccer, rugby, boxing, motor vehicles, etc., new tennis balls…) or liberation (e.g. squash balls, baseball bats, golf balls, etc.)

Must be able to understand/test collisions