Question

A 2-kg block is pushed against a spring with spring-constant k 512 N/m, compressing it 0.25 m. When the block is released, it moves along a frictionless, horizontal surface and then up a frictionless incline with slope 53.1° 

(a) What is the speed of the block as it slides along the horizontal surface after having left the spring? 

(b) How far does the block travel up the incline before starting to slide back down?

Answer 1

(a) The forces involved here (spring force, gravity) are conservative, so the total mechanical energy remains unchanged throughout the motion.

KE _{horizontal sliding} +PE _{horizontal sliding} = KE _{compressing spring} +PE _{compressing spring}

  

(b) At the top of its trajectory, the block will be momentarily at rest. In part (a) we implicitly chose the zero of gravitational potential energy to be at the horizontal surface. When the block travels a distance 'l' up the ramp, it will be a height 'l sinθ' above that origin.

KE _top +PE _top = KE _{compressing spring} + PE _{compressing spring}