You are designing a delivery ramp for crates containing exercise equipment. The
ID: 1633216 • Letter: Y
Question
You are designing a delivery ramp for crates containing exercise equipment. The 1650-N crates will move at 1.8 m/s at the top of a ramp that slopes downward at 22.0. The ramp exerts a 515-N kinetic friction force 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 5.0 m along the ramp. Once stopped, a crate must not rebound back up the ramp.
Calculate the largest force constant of the spring that will be needed to meet the design criteria.
Explanation / Answer
Use equation,
Work done by crate = dealKE + dealPE
W = dealKE + dealPE
W = Fk*d = - 515*5.0 = -2575 J
dealKE = 1/2*m(vf^2 - vi^2)
= 1/2*(W/g)*(0^2- 1.8^2)
= 1/2*(1650/9.8)(0 - 1.8^2)
= -272.75 J
dealPE = 1/2*kx^2 – m*g*h
= 1/2kx^2 – 1650*8sin22
= 1/2kx^2 – 4944.80 J
W = dealKE + dealPE
-2575 J = -272.75 J + 1/2kx^2 – 4944.80 J
kx^2 = 5281.11
Now Fs = m*g*sinq + Fk
= 1650*sin24 + 515
= 1186.11 N
k = (Fs)^2/kx^2
= (1186.2)^2/5281.11
= 226.3 N/m
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