What is the relationship between work, force, and displacement in a simple machine?

What is the relationship between work, force, and displacement in a simple machine?

• A. Work equals force times displacement in the direction of the force.
• B. Work equals force times velocity.
• C. Work is the energy transferred per unit time.
• D. Work equals distance times force.

Answer: (A)

Work is the transfer of energy that occurs when a force moves an object through a distance. Only the component of the force that acts along the direction of the motion contributes to that energy transfer. For a constant force along a straight path, the work done is the force component in the direction of the displacement times the distance moved, which simplifies to W = F d cos θ; when the force is aligned with the motion, this becomes W = F d. That makes the statement the best description: work equals force times displacement in the direction of the force. The other ideas mix in concepts from other physics: velocity is not a measure of work, but of rate of motion; energy transferred per unit time is power, not work; and simply multiplying distance by force ignores the angle between force and motion, which determines how much of the force actually does work.

Work is the transfer of energy that occurs when a force moves an object through a distance. Only the component of the force that acts along the direction of the motion contributes to that energy transfer. For a constant force along a straight path, the work done is the force component in the direction of the displacement times the distance moved, which simplifies to W = F d cos θ; when the force is aligned with the motion, this becomes W = F d.

That makes the statement the best description: work equals force times displacement in the direction of the force. The other ideas mix in concepts from other physics: velocity is not a measure of work, but of rate of motion; energy transferred per unit time is power, not work; and simply multiplying distance by force ignores the angle between force and motion, which determines how much of the force actually does work.