Question

Two blocks A and B of mass mA and mB , 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

The force exerted by the experimenter on block A  $F\left(1+\frac{m_{A}}{m_{B}}\right)$.

Explanation:

Step 1:

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

Let a be the acceleration the system produces.

in case of  block A,

$F^{\prime}-F=m_{A} a \quad \ldots \ldots \ldots e q^{n}(1)$

in case of  block B,

$\mathrm{F}=\mathrm{m}_{\mathrm{B}} \mathrm{a} \quad \ldots \ldots \ldots \ldots e q^{n}(2)$

Step 2:

Dividing equation (1) to (2), we obtain:

$\begin{aligned}&\frac{F^{\prime}}{F}-1=\frac{m_{A}}{\mathrm{m}_{\mathrm{B}}}\\&F^{\prime}=F\left(1+\frac{m_{A}}{\mathrm{m}_{\mathrm{B}}}\right)\end{aligned}$

The experimenter's force on block A is

$F\left(1+\frac{m_{A}}{m_{B}}\right)$

Answer 2

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