Answer to Question #123768 in Physics for Dr. Horus

Question

A parcel of mass 1kg is placed on a rough plane which is incline at 30° to the horizontal. The coefficient of friction between the parcel and the plane is 0.25. Find the force that must be applied to the parcel in a direction parallel to the plane. So that
(i) the parcel is just prevented from sliding down the plane.
(ii) the parcel is just on the point of moving up the plane.
(iii) the parcel move up the plane with an acceleration of 1.45m/s^2.

Answer 1

i)

$$F=mg\sin{30}-\mu mg\cos{30}\\=(1)(9.8)(\sin{30}-0.25 \cos{30})=2.8\ N$$

ii)

$$F=mg\sin{30}+\mu mg\cos{30}\\=(1)(9.8)(\sin{30}+0.25 \cos{30})=7.0\ N$$

iii)

$$F=mg\sin{30}+ma+\mu mg\cos{30}\\=(1)((9.8)(\sin{30}+0.25 \cos{30})+1.45)=8.5\ N$$