A particle with mass mA moves with a speed vA and collides w

A particle with mass m_A moves with a speed v_A and collides with a particles that the mass m_B (direct, elastic impact). If m_B >> m_A, calculate the velocities after the impact and v_B\'.

Solution

Determine the velocity of the particle B after the impact by using the following equation:

m_Av_A+m_Bv_B=m_Av_A^\'+m_Bv_B^\' ……(1)

Here, m_Aand m_Bare the masses of the particles A and B, v_Aand v_Bare the velocities before impact, and v_A^’and v_B^’are the velocities after impact.

As the mass of particle B is very large as compared to the particle A. Hence, the mass of the particle A is taken as zero.

Substitute 0 kg for m_A and 0 m/s for v_Bin equation (1).

0+0=0+v_B^’

v_B^’=0

Therefore, the velocity of the particle B after the impact is zero.

Calculate the velocity of the particle A after the impact by using the following equation:

e=-(v_B^’-v_A^’)/(v_B-v_A)   ……(2)

Here, e is the coefficient of restitution, v_Aand v_Bare the velocities of the particles before impact, and v_A^’and v_B^’are the velocities of the particles after impact.

For direct and elastic impact e=1.

Substitute 1 for e, 0 m/s for v_B and 0 m/s for v_B^’ in equation (2).

1=-(0-v_A^’)/ (0-v_A)

v_A^’= -v_A                                            (-ve sign indicates opposite direction)                                                               

Therefore, the particle A would rebound with the same velocity with which it strikes the particle B.