Question

A block of masses $\underrightarrow{m}$sliding on a smooth horizontal surface with a velocity v meets a long horizontal spring fixed at one end and having spring constant k as shown in figure (8-E 10).Find the maximum compression of tl spring. Will the velocity of the block be the same as $\overrightarrow{v}$ when it comes back to the original position shown ?

Answer 1

Let the compression be x

(a) According to law of conservation of energy

$\frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$

$\Rightarrow x^2=\frac{m{v}^2}{k}$

$x=v\sqrt{\left(\frac{m}{k}\right)}$

(b) No,It will be in the opposite direction and magnitude will be less due to loss in spring.