A block of mass m = 5.2 kg is released from rest at a height of H = 4.0 m on a curved frictionless ramp. At the foot of the ramp is a spring whose spring constant is k = 192.0 N/m. What is the maximum compression of the spring, x?

Question

A block of mass m = 5.2 kg is released from rest at a height of H = 4.0 m on a curved frictionless ramp. At the foot of the ramp is a spring whose spring constant is k = 192.0 N/m. What is the maximum compression of the spring, x? 
After the spring reaches its maximum compression, it pushes the block backwards. What is the maximum height reached by the block?

Thank's!

Elena · Answer

PE ->KE KE ->PE(spring) => PE= PE(spring) mgh=kx²/2 x=sqrt(2mgh/k)=… PE(spring) -> KE->PE => the same ‘h’ (due to the absence of friction)