# Designing a Delivery Ramp with Energy formulas

1. Oct 22, 2009

### am13

1. The problem statement, all variables and given/known data

You are designing a delivery ramp for crates containing exercise equipment. The crates of weight 1520 N will move with speed 2.2 m/s at the top of a ramp that slopes downward at an angle 22.0 degrees. The ramp will exert a 569 N force of kinetic friction on each crate, and the maximum force of static friction also has this value. At the bottom of the ramp, each crate will come to rest after compressing a spring a distance x. Each crate will move a total distance of 7.6 m along the ramp; this distance includes x. Once stopped, a crate must not rebound back up the ramp.

Calculate the maximum force constant of the spring kmax that can be used in order to meet the design criteria.

2. Relevant equations

Wext = Ef - Ei
Ug = mgh
KE = 1/2mv2
Us = 1/2kx2
Ff = mu * FN

3. The attempt at a solution

I tried setting Wext plus Ug plus KE equal to Us, but I don't know how to find x, the distance that the blocks stretch the spring, so that I can find k, nor do I know even if I am taking the right approach. (Can I treat all the crates as one crate?) Can anyone help me?