AP Physics, mechanical energy

Question

A block mass 2kg is moving at the speed of 4 m/s on a frictionless surface towards a spring. The spring has a spring constant of 20N/m

A.) How fast is the block going when it had compressed the spring.05

B.) what is the maximum compression caused by the block?

Answer 1

Conservation of energy problem

Block starts kinetic energy only = 1/2 mV²

when it being compressed, you have KE and PE due a spring, which is 1/2kX²

A.

1/2 2kg (4)² = 1/2 2kg V² + 1/2(20)(.05)²

solve for velocity

B.now you know there KE and Pe at x=.05

When is compressed fully, you have no KE, only PE due to spring.

So the velocity (V) in the a) part becomes your initial velocity. You can either use the conservation of energy formula or Work energy theorem Both will get you there but conservation of energy may be easier.

1/2mV² + 1/2 k(.05)² = 1/2k(xcompressed)²

solve for xcompressed