A 45 kg gymnast is bouncing on a trampoline. Model the gymnast as a particle and the trampoline as a spring with a spring constant of 15,000 N/m. The spring is compressed by 30 cm when the gymnast is at her lowest point. We want to determine how high she goes above the trampoline.

A spring with spring constant 29 N/m is compressed a distance of 9.0 cm by a ball with a mass of 206.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 9.0 cm and is also released, leaving the spring at point A. Each object travels up the incline shown in the figure before coming to rest momentarily. Assume the ball rolls, but ignore other effects of friction. (Assume the ball rolls without slipping up the incline until it comes to rest.)   (a) How high above the starting position is the ball when it comes to rest momentarily? m(b) How high above the starting position is the block when it comes to rest momentarily?

As shown in the figure below, a box of mass  m = 9.80 kg  is sliding across a horizontal frictionless surface with an initial speed  vi = 2.70 m/s  when it encounters a spring of constant  k = 2700 N/m.   The box comes momentarily to rest after compressing the spring some amount xc. Determine the final compression xc (in m) of the spring.

An 0.80-kg block is held in place against the spring by a 67-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v1=1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v2=1.9 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.39. The velocity of the block is v3=1.4 m/s at C. The block moves on to D, where it stops. The spring constant of the spring is closest to V2 V3 V4 A h smooth BErough C | ES >|

A spring with spring constant 23 N/m is compressed a distance of 8.0 cm by a ball with a mass of 219.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 8.0 cm and is also released, leaving the spring at point A. Assume the ball rolls, but ignore other effects of friction. (Assume that the ball is a solid ball.)   (a) What is the speed of the ball at point B?(b) What is the speed of the block at point B?

If a 4-kg block is placed against the spring and the spring is released, what will be the speed of the block when it separates from the spring at x =0? Neglect any friction in the problem.

You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1300 kgkg car moving at 0.66 m/sm/s is to compress the spring no more than 7.6×10−2 mm before stopping. 1. What should be the force constant of the spring? Assume that the spring has negligible mass. Express your answer using two significant figures.

It takes a flea 1.25 × 10−3 s to reach a peak speed of 0.757 m/s. Mass of the flea is 0.462 × 10−6 kg and insect muscle has a maximum output of 56.4 W/kg. If 20.0% of the flea’s weight is muscle, what is the muscular power output of the flea?

A 1.68-kg box rests atop a massless vertical spring with  k = 4170 N/m  that has been compressed by 14.2 cm from its equilibrium position. The box is released and leaves the spring when it reaches its equilibrium position. What is the maximum height the box reaches above its original position?

As shown in the figure below, a box of mass m = 8.00 kg is sliding across a horizontal frictionless surface with an initial speed v m/s when it encounters a spring of constant k = 2500 N/m. The box comes momentarily to rest after compressing the spring some amount x Determine the final compression x (in m) of the spring.