Find the speed and direction of the balls after collision.

Question

A 1.5 kg ball moving at 2 m/s to the right collides head on with a 1kg ball moving at 3 m/s to the left. The coefficient of restitution is 0.7.

Find the speed and direction of the balls after collision.

Answer 1

Let's find the initial momentum and it will be conserved.

p_initial = (1.5 kg * 2 m/s) + (1 kg * (-3 m/s)) = 0

P_initial = P_final = 0

Now, let's consider the coefficient of restitution, denoted as e. The coefficient of restitution represents the ratio of the relative velocity of separation to the relative velocity of approach after a collision. Mathematically, we can express it as follows:

e = (v_2f - v_1f) / (v_1i - v_2i)

0.7 = (v_2f - v_1f) / (2 m/s - (-3 m/s))

0.7 = (v_2f - v_1f) / 5 m/s

Now, we can solve for v_2f - v_1f:

3.5 m/s = v_2f - v_1f

p_final = m₁ * v_1f + m₂ * v_2f = 0

Substituting the given masses and final velocities, we have:

0 kg·m/s = (1.5 kg * v_1f) + (1 kg * v_2f)

Let's solve equations simultaneously;

v_2f - v_1f = 3.5

v_2f = -1.5 * v_1f

We solve and find as:

v_2f = 2.1 m/s

v_1f = -1.4 m/s