Difficulty: Easy
Correct Answer: g sin θ
Explanation:
Introduction / Context:
Resolving gravitational acceleration into components along and perpendicular to an inclined plane is a fundamental step in many statics and dynamics problems. With no friction, only the component of weight along the plane accelerates the block.
Given Data / Assumptions:
Concept / Approach:
Resolve weight W = m g into components: perpendicular to plane (m g cos θ) and along plane (m g sin θ). With no friction, the equation of motion along the plane is m a = m g sin θ, leading directly to a = g sin θ.
Step-by-Step Solution:
Verification / Alternative check:
Limiting cases: θ = 0° ⇒ a = 0; θ = 90° ⇒ a = g. Both agree with intuition.
Why Other Options Are Wrong:
g is the full vertical acceleration, not along the plane; g cos θ is the normal component; g tan θ is not a component of gravitational acceleration; zero would require θ = 0° or friction balancing, which is not the case here.
Common Pitfalls:
Using g cos θ for the along-plane component; forgetting to define axes parallel and perpendicular to the plane.
Final Answer:
g sin θ
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