Question

In a spring gun system, a spring with a spring force constant 370 N/m  , is compressed 0.13 m . When fired, 79.1% of the elastic potential energy stored in the spring is eventually converted into kinetic energy of a 5.50×10⁻² kg uniform ball that is rolling without slipping at the base of a ramp. The ball continues to roll without slipping up the ramp with 90.3 % of the kinetic energy at the bottom converted into an increase in gravitational potential energy at the instant it stops.

1.What is the velocity of the ball's center of mass at the base of the ramp?

2.At this position, what is the velocity of a point at the top of the ball?

3.What maximum vertical height up the ramp does the ball move?

Take the free fall acceleration to be 9.80m/s29.80m/s2.

Answer 1

Find the elastic potential energy stored in the spring,then find kinetic energy of the ball.90.3% of this kinetic energy is converted into the gravitational energy,So equate this part of energy to mgh to find the maximum height h.