Work classification by angle between force and displacement If the angle between an applied force and the actual direction of motion of a body lies between 90° and 180°, how is the work done by that force classified?

Introduction / Context:
Work is the energy transfer associated with a force acting through a displacement. The sign of work depends on the angle between the force vector and displacement vector, and recognizing the sign is crucial in energy methods and power calculations in mechanics.

Given Data / Assumptions:

• Force magnitude F acts while the body moves a displacement s.
• Angle θ between F and displacement satisfies 90° < θ ≤ 180°.
• Classical definition of work applies: W = F s cos θ for constant F and straight motion.

Concept / Approach:

The cosine of an angle between 90° and 180° is negative. Hence W = F s cos θ becomes negative. Physically, the force acts opposite to the motion’s component, removing energy from the system (e.g., friction opposing motion).

Step-by-Step Solution:

Verification / Alternative check:

Examples: kinetic friction on a sliding block (θ = 180°) always does negative work; a brake force opposing wheel motion is another common case.

Why Other Options Are Wrong:

(c) Zero work occurs only when θ = 90°. (a) Virtual work is a method, not a sign classification. (b) “Imaginary work” is not a standard term; (e) positive work requires θ < 90°.

Common Pitfalls:

Forgetting the vector dot product; mixing up power sign conventions with work sign.

Final Answer:

Negative work