Introduction and Question: You are designing a delivery ramp for crates containing exercise equipment. The crates weighing 1490 N will move at a speed of 1.80 m/s at the top of a ramp that slopes downward at an angle 21.0^\circ. The ramp exerts a kinetic friction force of 540 N on each crate, and the maximum static friction force also has this value. Each crate will compress a spring at the bottom of the ramp and will come to rest after traveling a total distance of 7.60 m along the ramp. Once stopped, a crate must not rebound back up the ramp. Calculate the force constant of the spring that will be needed in order to meet the design criteria. I am stuck on this only because I cannot extract from this data the distance the spring compresses. Can someone please offer some insight?
Possible one is to use two equations, with two unknowns, k and x. One is the force equation and the spring force, F_{sping} = kx, and the other equation is an energy equation, in which the spring stored energy is E_{sping}=1/2 kx^{2}.