Question

A delivery girl wishes to launch a 2.0-kg package up an inclined plane with sufficient speed to reach the top of the incline. The plane is 3.0 m long and is inclined at 20 degrees. The coefficient of kinetic friction between the package and the plane is 0.40. What minimum initial kinetic energy must the girl supply to the package?

Answer 1

Calculate the friction force between the lunch packet and the incline surface.

Fr = μ*mg*cosθ

= 0.4*2*9.81*cos20

= 7.37 N

Calculate the work done by the friction force.

WF = Fr *d

= 7.37 * 3

= 22.11 J

According the conservation of energy, the initial required kinetic energy of the lunch packet should be equal to the sum of the change in potential energy of the lunch packet and work done by the friction force.

(K.E)min =  WF + mgh

= 22.11 + 2*9.81*3

= 80.97 J

Thus, the minimum required kinetic energy of the block should be 80.97 J