A 20.0- k g crate sits at rest at the bottom of a 19.2 m -long ramp that is incl

Question

A 20.0-kg crate sits at rest at the bottom of a 19.2m -long ramp that is inclined at 34? above the horizontal. A constant horizontal force of 290 N is applied to the crate to push it up the ramp. While the crate is moving, the ramp exerts a constant frictional force on it that has magnitude 65.0 N.

Part A) is the total work done on the crate during its motion from the bottom to the top of the ramp?

Express your answer to three significant figures and include the appropriate units.

Part B)How much time does it take the crate to travel to the top of the ramp?

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

A) total work done

              = work done by gravity + work done by force + work done by friction

                = - 20 x 9.8 x 19.2sin34 + 290cos34 x 19.2 - 65 x 19.2

            = 1913.73 J

b) balancing forces :

290cos34 - 65 - 20gsin34 = 20a

a = 3.29 m/s2

h = ut + at^2 /2

19.2 = 0 + 3.29t^2 /2

t = 3.42 sec

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