Question

A block of mass $M$ slides on a frictionless surface with an initial speed of $v_{0}$. On top of block is a small box of mass $m$. The coefficients of friction between box and block are $\mu_{s}$ and $\mu_{k}$. The sliding block encounters an ideal spring with force constant $k$. Answer following questions.

Assuming no relative motion between box and block what is the maximum possible acceleration of block and box at the instant of maximum compression?

• A. $\mu_{s} g$
• B. $\frac{\mu_{s} M g}{m}$
• C. $\frac{\mu_{s}(M+m) g}{m}$
• D. $\frac{\mu_{s} m g}{M}$

Answer 1

Answer: (A)

$\left(\frac{1}{2} M+m\right) v_{0}^{2}=\frac{1}{2} k x_{m}^{2}$
$k x_{m}=\mu_{s} g$
$x_{m}=\mu_{s} k$
$(m+M) v_{0}^{2}=\frac{k \mu_{s}^{2} g^{2}}{k}$
$k=\left(\frac{\mu_{s} g}{v_{0}}\right)^{2}(M+m)$