Question

Two blocks A and B of mass m_A and m_B , respectively, are kept in contact on a frictionless table. The experimenter pushes block A from behind, so that the blocks accelerate. If block A exerts force F on block B, what is the force exerted by the experimenter on block A?

Answer 1

Let F' = force exerted by the experimenter on block A and F be the force exerted by block A on block B.

Let a be the acceleration produced in the system.

For block A,
$F\text{'}-F=m_{A}a$ ...(1)
For block B,
F = m_Ba ...(2)
Dividing equation (1) by (2), we get:
$\frac{F\text{'}}{F}-1=\frac{m_A}{m_B}$
$\Rightarrow F\text{'}=F\left(1+\frac{m_{\mathrm{A}}}{m_{\mathrm{B}}}\right)$
∴ Force exerted by the experimenter on block A is $F\left(1+\frac{m_{\mathrm{A}}}{m_{\mathrm{B}}}\right)$.