You are designing a delivery ramp for crates containing exercise equipment. The

Question

You are designing a delivery ramp for crates containing exercise equipment. The crates of weight 1417 N will move with speed 2.4 m/s at the top of a ramp that slopes downward at an angle 23.5 degrees. The ramp will exert a 565 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 7.27 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 k_max that can be used in order to meet the design criteria

Explanation / Answer

Kinetic energy K.E _f = mgh + 1/2 mv^2 - F_w

            To calculate the   height of the ramp we get

                 sin (23.6 ) = h / 7.27 m

                        h = 2.91 m

F = mg

1583 N = m * 9.8

mass m = 161.5

K.E_f = 161.5 kg * 9.8 * 2.91 m + 1/2 * 161.5 kg * ( 1.98 m/s )^2 - 633 N

            = 4290 J

K.E = P.E

4290 J = 1/2 k x^2

       k = 8580/ x^2

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