The equation for elastic potential energy is elastic PE=1/2 kx^2 where x is the distance the spring was stretched or compressed from its equilibrium point, and k is the spring stiffness constant which varies with each spring. The amount of force required to stretch or compress a spring is given by F = kx.

A. A 75-kg trampoline artist jumps vertically upward from the top of a platform that is 5m above the trampoline at a velocity of 6.7m/s. How fast is she going as she lands on the trampoline? And if the trampoline behaves like a spring with a spring stiffness constant of 5.1 x 104 N/m, how far does she depress the trampoline, or stretch it downwards?

B. Use a free-body diagram and the conservation of energy to answer this question. A 0.700kg wood block is firmly attached to a very light horizontal spring which has a spring stiffness constant of 210N/m. The block-spring system, when compressed 6.2cm and then is released, stretches 2.8cm beyond the equilibrium point (the zero potential energy point) before turning back. What is the coefficient of kinetic friction between the block and the table? Hint: Remember Ffr opposes motion and so in this scenario acts against the block's stretching motion when the block-spring system is released.

C. Scales that measure weight have springs inside of them that allow for measurement of the normal force the scale exerts on the person (or object) as they stand (or lie) on the scale. If you stand on a bathroom scale, the spring inside the scale compresses 0.70mm and the scale says your weight is 680N. Now if you jump on the scale from a height of 0.8m, what does the scale read at its peak weight? Assume no energy is lost as thermal energy due to air resistance or friction. Hint: you will need the quadratic equation. Use conservation of energy rather than forces and a free body diagram.