Answer:
Mass of the box = 0.9433 kg
Explanation:
Mass of racket-ball [tex](m_1)[/tex] = 0.00427 kg
Velocity of racket-ball before collision [tex](v_{1i})[/tex] = 22.3 m/s
Velocity of racket-ball after collision with box [tex](v_{1f})[/tex] = -11.5 m/s
[Since ball is bouncing back, so velocity is taken negative.]
Velocity of the box before collision [tex]v_{2i}[/tex] = 0 m/s
[Since the box is stationary, so velocity is taken zero]
Velocity of box moving forward after collision [tex]v_{2f}[/tex]= 1.53 m/s
To find the mas of the box [tex]m_2[/tex].
By law of conservation of momentum we have:
Momentum before collision = Momentum after collision
This can be written as:
[tex]p_i=p_f[/tex]
[tex]m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}[/tex]
We can plugin the given value to find [tex]m_2[/tex]
[tex](0.0427\times 22.3)+(m_2\times 0)=(0.0427\times (-11.5))(m_2\times 1.53)[/tex]
[tex]0.9522+0=-0.4911+1.53m_2[/tex]
Adding both sides by 0.4911
[tex]0.9522+0.4911=-0.4911+0.4911+1.53m_2[/tex]
[tex]1.4433=1.53m_2[/tex]
Dividing both sides by 1.53.
[tex]\frac{1.4433}{1.53}=\frac{1.53m_2}{1.53}[/tex]
[tex]0.9433=m_2[/tex]
∴ [tex]m_2=0.9433[/tex] kg
Mass of the box = 0.9433 kg (Answer)
