Problem 1) A 20.0 crate sits at rest at the bottom of a 150-m-long ramp that is

Question

Problem 1) A 20.0 crate sits at rest at the bottom of a 150-m-long ramp that is inclined at 34.00 above horizontal A constant horizontal force of 290 N is applied to the crate to push it up the ramp. While the crate is e ramp exerts a constant frictional force on it that has magnititude 65.O N a) What b) s the total work done on the crate during its motion from the bottom to the top of the ramp? How much time does it take the crate to travel to the top of the ramp? at is the coefficent of friction between the crate and the ramp? c) Wh 15.0 m 34.0

Explanation / Answer

(A) total work done = Work done by gravity + work done by force + work done byfriction.

W = (- m g h) + (F x ) + (- f L)

W = (-20 x 9.8 x 15 sin34) + (290 x 15 cos34) + (-65 x 15)

W = 987.3 J

(B) work done = change in Ke

987.3 = 20 v^2 / 2

v = 9.94 m/s

Applying vf^2 - vi^2 =2 a d

9.94^2 - 0^2 = 2(15)(a)

a = 3.29 m/s^2

vf = vi + a t

9.94 = 0 + 3.29 t

t = 3.02 sec

(C) f = 65 N

N = m g cos34 = 162.5 N

u = f/N = 0.40

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