A box is on a ramp that is at angle θ to the horizontal. As θ is increased from zero, and before the box slips, do the following increase, decrease, or remain the same: (a) the component of the gravitational force on the box, along the ramp, (b) the magnitude of the static frictional force on the box from the ramp, (c) the component of the gravitational force on the box, perpendicular to the ramp, (d) the magnitude of the normal force on the box from the ramp, and (e) the maximum value fs, max of the static frictional force?

a) Increases.

b) Decreases.

c) Decreases.

d) Decreases.

e) Decreases.

Explanation:

The forces acting on the box and the resolving of the forces are shown in the attached image to the question.

From the balance, the normal reaction = mg cos θ

a) The component of the gravitational force on the box, along the ramp is given by mg sin θ

As θ increases from 0, this component also increases (since sin θ increases)

b) At θ = 0, the frictional force is μN, but as θ gains in value, it becomes smaller.

Indicating a decrease in value as θ increases until the box slips.

c) the component of the gravitational force on the box, perpendicular to the ramp is mg cos θ and it decreases from the maximum at (mgcos 0 = mg) to mg cos θ.

d) The normal reaction = mg cos θ and this decreases from mg at 0 to whatever value as θ increases. Normal reaction decreases.

e) The maximum value fs, max of the static frictional force also decreases as θ increases. It decreases from (μmg cos 0) to (μmg cos θ) as θ goes from 0 to θ.