A child of mass 32 kg jumps up and down on a trampoline. The trampoline exerts a spring restoring force on the child with a spring constant of N/m. At the highest point of the bounce, the child is 1.0 m vertically above the unstretched surface level of the trampoline. What distance is the trampoline compressed by when the child jumps on it? Neglect the bending of the child’s legs or any transfer of energy of the child into the trampoline while jumping.
A pogo stick has a spring constant of N/m. A child stands on the pogo stick, pointing the stick vertically upward and compressing it by 12.0 cm. The child and pogo stick have a combined mass of 40.0 kg. The child jumps, which exerts negligible force but causes the pogo stick to return to its equilibrium length. What is the maximum upward vertical displacement of the child?
In a Coyote/Road Runner cartoon clip, a spring expands quickly and sends the coyote into a rock. The spring extends by 5.0 m and accelerates the coyote of mass 20 kg to a speed of 15 m/s.
What is the spring constant of this spring?
If the coyote were sent vertically upward with the energy given to him by the spring, what maximum height would it reach, assuming air resistance was negligible?
In the movie Monty Python and the Holy Grail, a cow of mass 110 kg is catapulted from the top of a castle wall 9.1 m high, onto the people down below. The cow is launched from a spring of with a constant of N/m that was initially compressed by 0.50 m from equilibrium. The gravitational potential energy is set to zero at the base of the castle wall.
What is the gravitational potential energy of the cow as it just clears the castle wall, treating the cow as a point particle?
What is the elastic spring energy of the cow before the catapult is released?
What is the speed of the cow at the instant that it hits the ground?
A box that has 50 J of kinetic energy slides on a frictionless surface. The box hits a spring and compresses the spring a distance of 25 cm from its equilibrium length. If the same box with the same initial energy slides on a rough surface, it only compresses the spring a distance of 15 cm. How much energy must have been lost by the box when sliding on the rough surface?