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 . 4 k g . The object is initially at rest at the top of a slope with an angle 𝜃 = 5 0 ∘ , 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 . 5 c m along the slope, where it has an instantaneous speed 𝑣 = 0 . 8 5 / m s . Find the friction force acting on the object.

Q2:

An object has a mass 𝑚 = 1 . 8 k g . The object is on a slope with an angle 𝜃 = 4 2 ∘ , 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 . 5 k g . The object is initially moving at a speed 𝑢 = 1 . 2 / m s parallel to a slope with an angle 𝜃 = 2 9 ∘ , as shown in the diagram. The surface of the slope produces friction with the base of the object. The object’s upward displacement 𝑠 = 1 1 c m 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 . 2 k g . The object is at rest on a slope with an angle 𝜃 = 4 8 ∘ , 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 / m s parallel to a smooth slope with an angle 𝜃 , as shown in the diagram. The object’s upward displacement 𝑠 = 1 8 c m 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 = 3 6 ∘ , as shown in the diagram. The object’s upward displacement 𝑠 = 7 . 2 c m 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?

  • A 𝑅 = − 𝑊
  • B 𝑅 = 𝑊
  • C 𝑅 = 𝑊 ( 𝜃 ) s i n
  • D 𝑅 = ( 𝜃 ) 𝑊 s i n
  • E 𝑅 = 𝑊 ( 𝜃 ) c o s

What is the magnitude of 𝑅 if the angle of the slope above the horizontal is 9 0 ∘ ?

Q8:

An object has a mass 𝑚 = 1 . 3 k g . 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 . 8 c m along the slope, where it has an instantaneous speed 𝑣 = 0 . 7 2 / m s . Find 𝜃 .

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