Question

1. Consider a head-on collision between two identical billiard balls. Ball 1 is initially in motion toward ball 2, which is initially at rest. After the collision, ball 2 departs with the same velocity that ball 1 originally had. Disregard any friction between the balls and the surface. What happens to ball 1? What happens to ball 2?

Answer 1

Answer:

Ball 1 is at rest after the collision, while ball 2 carries all the momentum, with a velocity equal to what ball 1 had initially previous to the collision.

Explanation:

We analyze the conservation of momentum for the total momentum of the two billiard ball system, before (initial) and after (final) the collision:

$P_i=m_1\,v_i+ m_2\,(0)\\P_i=m_1\,v_i$

Now we write the final momentum of the system, knowing from the given information that ball 2 departs with the same velocity that ball 1 had initially, but not knowing what velocity ball 1 has (using the symbol  $v_f$ to describe it):

$P_f=m_1\,v_f +m_2\,v_i$

so now we use the fact that the two balls are identical (they have same mass "m") and also use the conservation of momentum (Pi = Pf)

to solve for the unknown velocity ( $v_f$ ) of ball 1:

$P_i=P_f\\m\,v_i = m\,v_f+m\,v_i\\m\,v_i -m\,v_i =m\,v_f\\0=m\,v_f\\v_f= \frac{0}{m} \\v_f=0$

So we found that ball 1 has zero velocity (is now at rest) and therefore has transferred all the momentum it initially carried, to ball 2.

Answer 2

Answer:

first ball is at rest after collision and the kinetic energy of the first ball is transferred to the second ball after collision.

Explanation:

mass of each ball = m

initial velocity of first ball = u

initial velocity of second ball = 0 m/s

final velocity of second ball = initial velocity of first ball = u

Use conservation of momentum

let v is the final velocity of the first ball after collision

m x u + m x 0 = m x v + m x u

So, v = 0

It means after the collision the second ball moves with the velocity which is equal to the initial velocity of the first ball and the first ball comes at rest.

As there is no friction between the balls during the collision, the collision of two balls is perfectly elastic and thus the kinetic energy of the system is conserved.

The entire kinetic energy of the first ball is transferred to the second ball after the collision.