Definition of mechanical work: In basic engineering mechanics, how is work defined for a constant force acting along its line of action?

Introduction / Context:

Work quantifies the energy transfer when a force causes a displacement. This concept underpins power calculations, efficiency assessments, and energy methods in structures and machines.

Given Data / Assumptions:

• Constant force F acting along the direction of motion.
• Displacement s measured along the line of action.
• No changes in direction or variable forces (for this definition).

Concept / Approach:

For a constant, collinear force and displacement, work W is the scalar product of force and displacement: W = F * s. In the general case with an angle θ between force and displacement, W = F * s * cos θ; here θ = 0°, so cos θ = 1.

Step-by-Step Solution:

Verification / Alternative check:

Energy perspective: the change in kinetic energy equals the net work done (work–energy theorem), which reduces to F * s for a constant net force.

Why Other Options Are Wrong:

• Force x velocity equals power, not work.
• Force x acceleration is not a standard energy quantity and has units inconsistent with energy.
• “None of these” is false because the correct definition is provided.

Common Pitfalls:

• Ignoring direction: only the component of force along the displacement does work.

Final Answer:

force x distance