Question

A $520$ gram block is sliding to the right on a surface that exerts a frictional force with coefficient of kinetic friction $\mu =0.400$. It collides with a horizontal spring with spring constant $k=18.0kg/s^2$ which compresses by $12.0cm$ as the block comes to rest.
What was the initial speed of the block?

• A. $0.706m/s$
• B. $0.970m/s$
• C. $1.20m/s$
• D. $1.44m/s$
• E. Not enough information

Answer 1

Answer: (C)

$1.20m/s$

From the conservation of work-energy, the initial kinetic energy of block goes into the work done against friction and potential energy in compression of spring.

$⟹\frac{1}{2}m{v}^2=\mu mgd+\frac{1}{2}k{d}^2$

$⟹v=\sqrt{2\mu gd+\frac{k}{m}{d}^2}$

$=1.20m/s$

Hence correct answer is option C.