Chapter 11, Problem 90A

To determine

To Calculate: Mass of object A.

Answer to Problem 90A

  $m_A=0.67\text{ kg}$

Explanation of Solution

Given info:

Mass of object B, $m_B=2.0\text{ kg}$

Initial speed of object A, $u_A=3.2\text{ m/s}$

Initial speed of object B, $u_B=0$

Speedof A after collision, $v_A=-v$

Speed of B after collision, $v_B=v$

Formula used:

Conservation of momentum:

  $p_i=p_f$

Coefficient of restitution:

  $e=\frac{v_B-v_A}{u_A-u_B}$

Calculation:

Mass of object A, $m_A=?$

Applying the conservation of momentum:

  $m_A{u}_A+m_B{u}_B=m_A{v}_A+m_B{v}_B$

Plugging in the given values:

  $\begin{array}{l}{m}_A\times 3.2+2.0\times 0=m_A\times \left(-v\right)+2.0\times v\\ 3.2m_A=-m_{A}v+2v\mathrm{.................}\text{(i)}\end{array}$

Since, collision is completely elastic, therefore coefficient of restitution would be 1:

  $1=\frac{v-\left(-v\right)}{\begin{array}{c}3.2-0\\ 2v=3.2\\ v=\frac{3.2}{2}\\ =1.6\text{ m/s}\end{array}}$

Plugging in the value of $v$ in equation (i):

  $\begin{array}{c}3.2\times m_A=-m_A\times 1.6+2\times 1.6\\ 4.8m_A=3.2\\ m_A=0.67\text{ kg}\end{array}$

Conclusion:

Mass of object A: $0.67\text{ kg}$