Question

A puck is attached to an unstretched ideal spring which is attached by its other end to a wall. The puck is pulled away from the wall along a frictionless horizontal surface, stretching the spring. The puck is then released, causing it to accelerate toward the wall.
By the time the puck is back to the location where the spring is stretched half as much as when the puck was released, how much kinetic energy does the puck have, compare to how much it will have when it reaches the position where the spring was unstretched?

• A. $1/2$ as much
• B. $1/4$ as much
• C. $2$ times as much
• D. $3/4$ as much
• E. $4/5$ as much

Answer 1

The correct option is D $3/4$ as much

This a spring-mass system , which is under SHM , and kinetic energy in a SHM is given by ,

$K=1/2k(a^2-y^2)$ ,

where $k=$ spring constant ,

$a=$ amplitude ,

$y=$ distance of mass from mean position ,

when puck is at half distance from full stretch , $y=a/2$

$K_1=1/2(a^2-(a/2{)}^2)=1/2(3a^2/4)$ ................eq1 ,

when puck is at the position where spring was unstretched , , $y=0$

$K_2=1/2(a^2-0^2)=1/2\left(a^2\right)$ ................eq2 ,

dividing eq1 by eq2 ,

$K_1/K_2=3/4$