You are designing a delivery ramp for crates containing exercise equipment. The crates weighing 
will move at a speed of 
at the top of a ramp that slopes downward at an angle 
The ramp exerts a kinetic friction force of 
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 
along the ramp. Once stopped, a crate must not rebound back up the ramp.
Question:
Calculate the force constant of the spring that will be needed in order to meet the design criteria.
My answer is 27.4 N/m, but I am not quite sure that it is correct.
I know
is zero.
is also zero.
is
. I define
.
So, I should use the equation
.
. But, it is -3.21 because
is below
.
Using the equation I believe I should use, I got the answer to be
