First slide

Work done by Diff type of forces

Question

Two plates whose masses are m₁ and m₂ respectively are connected by a massless spring as shown in figure. What minimum force should be applied to the upper plate for it to lift the lower one after the force is removed.

Moderate

A

(m₁ + m₂) g
B

(2m₁ + m₂) g
C

(m₁ + 2m₂) g
D

2(m₁ + m₂) g

Solution

The lower plate will rise if spring force on it greater than its weight ${Kx}_{2} > m_{2} g$
suppose it is compressed by $x_{1}; \frac{1}{2} {Kx}_{1}^{2} = \frac{1}{2} {Kx}_{2}^{2} + m_{1} g (x_{1} + x_{2})$
$Hence x_{1} > \frac{2 m_{1}}{K} g + \frac{m_{2} g}{K} \begin{aligned} F + m_{1} g = {Kx}_{1} \\ F > (m_{1} + m_{2}) g \end{aligned}$

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