Question

Write an expression for the work done by the spring? (Physics)

Answer 1

`(mgD^2)/(4h)`

Explanation:

The time it takes for the block to drop through a height `h` is given by `sqrt((2h)/g)`. In this time, it has traveled a horizontal distance `D` . So, the vertical component of the speed, which is the speed with which the block is launched from the table, is given by

`v_0 = Dsqrt(g/(2h))`

Thus the work done by the spring, which by the work energy theorem is the kinetic energy of the block when it was launched, is given by

`1/2mv_0^2 = 1/2 mD^2 g/(2h) = (mgD^2)/(4h)`