Question

Two cars initially at rest are free to move in the $x$ direction. Car $A$ has mass $4kg$ and car $B$ has mass $2kg$. They are tied together, compressing a spring in between them. When the spring holding them together is burned, car $A$ moves off with a speed of $2m/s$. How much energy in $joules$ was stored in the spring before it was burned?

Answer 1

As the force on each car due to Spring is same. Therefore at any instance the acceleration of car B$=2\times$acceleration of car A

Speed of B when spring burned off$=2\times 2=4m/s$

Energy Balance:

Initial Potential Energy= Final Kinetic Energy$=0.5\times 4\times \left(2^2\right)+0.5\times 2\times \left(4^2\right)=24joules$

energy stored in the spring before it was burned $=24joules$