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 𝑚=1.4kg. The object is initially at rest at the top of a slope with an angle 𝜃=50∘, as shown in the diagram. The surface of the slope produces friction with the base of the object. The object’s downward displacement 𝑠=5.5cm along the slope, where it has an instantaneous speed 𝑣=0.85/ms. Find the friction force acting on the object.

Q2:

An object has a mass 𝑚=1.8kg. The object is on a slope with an angle 𝜃=42∘, as shown in the diagram. The surface of the slope produces friction with the base of the object. The acceleration 𝑎 of the object parallel to the surface of the slope is 5.4 m/s2. What is the magnitude of the friction force?

Q3:

An object has a mass 𝑚=1.5kg. The object is initially moving at a speed 𝑢=1.2/ms parallel to a slope with an angle 𝜃=29∘, as shown in the diagram. The surface of the slope produces friction with the base of the object. The object’s upward displacement 𝑠=11cm 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 𝑚=2.2kg. The object is at rest on a slope with an angle 𝜃=48∘, 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 𝑢=1.4/ms parallel to a smooth slope with an angle 𝜃, as shown in the diagram. The object’s upward displacement 𝑠=18cm along the slope before it is instantaneously at rest on the slope. Find 𝜃.

Q6:

An object is initially moving at a speed 𝑢 parallel to a smooth slope with an angle 𝜃=36∘, as shown in the diagram. The object’s upward displacement 𝑠=7.2cm along the slope before it is instantaneously at rest on the slope. Find 𝑢.

Q7:

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

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

  • A𝑅=𝑊
  • B𝑅=𝑊(𝜃)sin
  • C𝑅=−𝑊
  • D𝑅=(𝜃)𝑊sin
  • E𝑅=𝑊(𝜃)cos

What is the magnitude of 𝑅 if the angle of the slope above the horizontal is 90∘?

Q8:

An object has a mass 𝑚=1.3kg. The object is initially at rest at the top of a slope with an angle 𝜃, 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 𝑠=3.8cm along the slope, where it has an instantaneous speed 𝑣=0.72/ms. Find 𝜃.

Q9:

An object has a mass 𝑚=1.3kg. The object is on a smooth slope with an angle 𝜃=33∘, as shown in the diagram. What is the acceleration 𝑎 of the object parallel to the surface of the slope?

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