An object rests on an inclined slope. Which of the following statements is true?

Question

BlackTom AI · Accepted Answer

For an object at rest on an incline the equilibrium of forces is the key idea: the vector sum of all forces must be zero.

1) Relevant concepts
- Weight (mg) acts vertically downward.
- Resolve weight into two components relative to the plane: perpendicular component mg cosθ and parallel (down-slope) component mg sinθ.
- The slope exerts a normal force N perpendicular to the surface and a static friction force f parallel to the surface (opposing motion).
- For the object to remain at rest, net force in both perpendicular and parallel directions must be zero.

2) Step-by-step reasoning and calculations
- Perpendicular direction: Sum of forces = 0 ⇒ N − mg cosθ = 0, so N = mg cosθ.
- Parallel direction (along the slope): Sum of forces = 0 ⇒ f − mg sinθ = 0 (taking up-slope friction positive), so f = mg sinθ.
- Combining these shows that the two contact forces (normal and friction) exactly balance the corresponding components of the weight, which means the total vector sum of forces is zero: N (perpendicular) + f (parallel) + mg (downward) = 0 vector.

3) Intermediate steps shown
- Weight components: W⊥ = mg cosθ, W∥ = mg sinθ.
- Equilibrium: N = W⊥, f = W∥ ⇒ net force = 0.

4) Why the correct answer is correct
- Statement (a) “The net force acting on the object is equal to zero” correctly states the equilibrium condition for a resting object. The detailed decomposition above shows all force components cancel, giving zero net force.

5) Why the other options are incorrect
- (b) “The object weight force is balanced by the friction force” is false: friction balances only the down-slope component mg sinθ, not the entire weight vector mg.
- (c) “The object weight force is balanced by the normal force” is false: the normal balances only the perpendicular component mg cosθ, not the full weight.
- (d) “The friction force is balanced by the normal force” is false: friction and normal act in perpendicular directions and do not balance each other.

Conclusion: The correct choice is (a). This matches the provided answer.

An object rests on an inclined slope. Which of the following statements is true?单项选择题

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An object rests on an inclined slope. Which of the following statements is true?

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