A box of mass 150kg must be pushed up a ramp that makes a 15 degree angle with t

Question

A box of mass 150kg must be pushed up a ramp that makes a 15 degree angle with the floor and the coefficient of static friction between the box and the floor is 0.700 and the coefficient of kinetic friction is 0.300. If your worker can push with a force 550.0N can he get the box to move up the ramp from the position shown? If so what is the acceleration of the box up the incline plane and if the distance along the ramp is 2.50m what speed is the box going as it reaches the top assuming you are starting from rest?

Explanation / Answer

Here ,

let the acceleration of the box is a

Using second law of motion

using the maximum static friction

Fnet = 550 - 150 * 9.8 * sin(15) - 0.6 * 150 * 9.8 * cos(15)

Fnet = -682 N

as the force is negative , this force is not enough to move the box up the ramp

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