Unless otherwise stated, all objects are located near the Earth's surface, where g = 9.80 m/s2 . A block of mass 26.0 kg slides down a frictionless surface inclined at 31 ∘.

Question

Part A

To ensure that the block does not accelerate, what is the magnitude of the smallest force that you must exert on it?

Express your answer using two significant figures.

Part B

What is its direction?

up the incline

down the incline

Answer 1

Part A.

Because the surface is frictionless, only 2 forces act on the body: weight mg - vertically down and normal reaction force N which is perpendicular to the surface of the incline. Those 2 forces will cause the body to move down incline with the acceleration a = gsinΘ, where g - acceleration of free fall and Θ = 31° - angle of inclination of the surface. To prevent the motion of the body, external force must be applied. This force could have different direction, but because we are looking for the force of smallest magnitude, its direction will be opposite to sliding direction, i.e., up the incline and parallel to it.

Selecting the x-axis parallel to incline and down, we write:

mgsinΘ - F = 0 or F = mgsinΘ

Plugging in the values of all variables, we obtain for the minimum force

F = 26.0 kg x 9.8 m/s² x sin 31° = 131.2 N

Answer: the magnitude of the smallest force 131.2 N

Part B. As we discussed already, the direction of this force is up the incline.

Answer: the direction of the force is up the incline