How does mass affect the outcome of a head-on elastic collision?

[phyzwiz69]

Homework Statement

A rapidly moving body of mass m1 strikes a body of mass m2 at rest in a head-on elastic collision. How does m1 compare with m2 if the first body (m1)
a. stops?
b. comes back along its path at very nearly the same speed it had before the collision?
c. continues along in the same direction with very nearly the same speed that it had before the collision?
d. comes back along its path with a very small speed?
e. continues along its path with a very small speed?

Homework Equations

The Attempt at a Solution

 

[fatra2]

Hi there,

The two laws of conservation will help you solve this problem: energy conservation, and momentum conservation.

Cheers

 

[kerimek]

In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum before the collision is equal to the total momentum after the collision, and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

a. When the first body (m1) stops, it means that all of its kinetic energy has been transferred to the second body (m2). This suggests that m2 is larger than m1, as it was initially at rest and now has all the kinetic energy.

b. When the first body (m1) comes back along its path at very nearly the same speed it had before the collision, it means that the two bodies have exchanged momentum and kinetic energy. This suggests that m1 and m2 are equal in mass.

c. When the first body (m1) continues along in the same direction with very nearly the same speed it had before the collision, it means that m1 has retained most of its initial momentum and kinetic energy. This suggests that m1 is much larger than m2, as it was able to maintain its speed and direction after the collision.

d. When the first body (m1) comes back along its path with a very small speed, it means that most of its kinetic energy has been transferred to m2. This suggests that m2 is larger than m1, as it was initially at rest and now has all the kinetic energy.

e. When the first body (m1) continues along its path with a very small speed, it means that most of its kinetic energy has been transferred to m2, but m1 still has some residual momentum and kinetic energy. This suggests that m1 is slightly smaller than m2, as it was able to maintain some of its initial energy and momentum.