# Crates on a Ramp with Friction and a spring at bottom. Finding the spring constant.

1. Jul 14, 2009

### Brainsplosion

You are designing a delivery ramp for crates containing exercise equipment. The crates weighing $F_1$ will move at a speed of v at the top of a ramp that slopes downward at an angle $\phi$. The ramp exerts a kinetic friction force of $F_2$ 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: $(Lsin\phi)F_1+1/2*mv^2$
final energy: $1/2*kx^2$
lost energy: $F_2L$

initial= final + lost
$(Lsin\phi)F_1+1/2*mv^2 = 1/2*kx^2 + F_2L$ (we shall call this equation 1)

From the free body diagram of the crate resting on the spring at the bottom of the ramp:
$kx=F_1sin\phi+F_2$ (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 $F_1/g$ ?
Then, am I supposed to solve for x in equation 2 then plug that into equation 1?

Last edited by a moderator: May 4, 2017
2. Jul 14, 2009

### LowlyPion

Re: Crates on a Ramp with Friction and a spring at bottom. Finding the spring constan

Looks like a plan.

F1/g looks workable.

2 equations, 2 unknowns ...

3. Jul 15, 2009

### Brainsplosion

Re: Crates on a Ramp with Friction and a spring at bottom. Finding the spring constan

Edit: I found what I was doing wrong. Thanks.

Last edited: Jul 15, 2009