# Worksheet: Normal Reaction Force on a Sloping Surface

In this worksheet, we will practice analyzing weight, friction, and normal reaction forces contributing to the motion of objects on sloped surfaces.

**Q1: **

An object has a mass . The object is initially at rest at the top of a slope with an angle , as shown in the diagram. The surface of the slope produces friction with the base of the object. The object’s downward displacement along the slope, where it has an instantaneous speed . Find the friction force acting on the object.

**Q2: **

An object has a mass
.
The object is on a slope
with an angle ,
as shown in the diagram. The surface of the slope produces
friction with the base of the object. The acceleration of the object
parallel to the surface of the slope is
5.4 m/s^{2}. What is the
magnitude of the friction force?

**Q3: **

An object has a mass . The object is initially moving at a speed parallel to a slope with an angle , as shown in the diagram. The surface of the slope produces friction with the base of the object. The object’s upward displacement along the slope before it is instantaneously at rest on the slope. Find the magnitude of the friction force.

**Q4: **

An object has a mass . The object is at rest on a slope with an angle , as shown in the diagram. The surface of the slope produces friction with the base of the object. What is the magnitude of the friction force on the object?

**Q5: **

An object is initially moving at a speed parallel to a smooth slope with an angle , as shown in the diagram. The object’s upward displacement along the slope before it is instantaneously at rest on the slope. Find .

**Q6: **

An object is initially moving at a speed parallel to a smooth slope with an angle , as shown in the diagram. The object’s upward displacement along the slope before it is instantaneously at rest on the slope. Find .

**Q7: **

A point mass is on a slope, as shown in the diagram. The weight of the mass, , and the normal reaction force, , act on the point mass.

What is the relationship between and if the angle of the slope above the horizontal is zero?

- A
- B
- C
- D
- E

What is the magnitude of if the angle of the slope above the horizontal is ?

**Q8: **

An object has a mass . The object is initially at rest at the top of a slope with an angle , as shown in the diagram. The surface of the slope produces a friction force of magnitude 2.2 N with the base of the object. The object’s downward displacement is along the slope, where it has an instantaneous speed . Find .

**Q9: **

An object has a mass . The object is on a smooth slope with an angle , as shown in the diagram. What is the acceleration of the object parallel to the surface of the slope?