You are designing a delivery ramp for crates containing exercise equipment. The crates weighing [itex]F_1[/itex] will move at a speed of v at the top of a ramp that slopes downward at an angle [itex]\phi[/itex]. The ramp exerts a kinetic friction force of [itex]F_2[/itex] 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 L 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. http://img269.imageshack.us/img269/1397/asdfbjl.png [Broken] This is what I've tried so far: initial energy: [itex](Lsin\phi)F_1+1/2*mv^2[/itex] final energy: [itex]1/2*kx^2[/itex] lost energy: [itex]F_2L[/itex] initial= final + lost [itex](Lsin\phi)F_1+1/2*mv^2 = 1/2*kx^2 + F_2L[/itex] (we shall call this equation 1) From the free body diagram of the crate resting on the spring at the bottom of the ramp: [itex]kx=F_1sin\phi+F_2[/itex] (we shall call this equation 2) I'm not quite sure all of the above is correct, but if so.. I don't think there's supposed to be the variable of m in there. Should I substitute [itex]F_1/g[/itex] ? Then, am I supposed to solve for x in equation 2 then plug that into equation 1?