Question

Two blocks of masses $m_{1}and{m}_2$ connected by a light spring rest on a horizontal plane. The coefficient of friction between the blocks and the surface is equal to $\mu$. What minimum constant force has to be applied in the horizontal direction to the block of mass $m_1$ in order to shift the other block?

• A. $(m_1+\frac{m_2}{2})\mu g$
• B. $(m_1+\frac{m_2}{3})\mu g$
• C. $(m_1+\frac{3m_2}{2})\mu g$
• D. $(2m_1+\frac{m_2}{2})\mu g$

Answer 1

Answer: (A)

$(m_1+\frac{m_2}{2})\mu g$

For the block of mass $m_2$ to just move, $\mu m_{2}g=kx$.

Conservation of energy for the first block gives,

$Fx=\mu m_{1}gx+\frac{1}{2}k{x}^2$

$⟹F=(m_1+\frac{m_2}{2})\mu g$