On a horizontal plane with no vertical displacement, which statement is true about work done by forces on the moving object?

On a horizontal plane with no vertical displacement, which statement is true about work done by forces on the moving object?

• A. Gravity does work
• B. Normal does work
• C. Friction does not do work
• D. Forces with a component in the direction of motion do work

Answer: (D)

The key idea is that work depends on how much of the force actually points along the direction of the object's displacement. Work, in math terms, is the dot product F · d, which means only the component of a force in the direction of the motion contributes to work. Here the motion is horizontal, so the displacement is along a horizontal line. Gravity acts straight down and the normal force acts straight up; both are perpendicular to the movement, so their dot product with the displacement is zero. That means gravity and the normal do no work on the object in this situation. Friction, on the other hand, acts along the surface. If the object is moving, friction acts opposite to the direction of motion, giving it a component in the direction opposite to displacement. That results in negative work by friction (it reduces the object's kinetic energy). More generally, any force that has a component in the direction of motion will do work (positive if it points forward with the motion, negative if it points backward). So the statement that captures the general rule—forces with a component in the direction of motion do work—is the correct one. Gravity and the normal do no work here, while friction does work (negatively) when there is motion.

The key idea is that work depends on how much of the force actually points along the direction of the object's displacement. Work, in math terms, is the dot product F · d, which means only the component of a force in the direction of the motion contributes to work.

Here the motion is horizontal, so the displacement is along a horizontal line. Gravity acts straight down and the normal force acts straight up; both are perpendicular to the movement, so their dot product with the displacement is zero. That means gravity and the normal do no work on the object in this situation.

Friction, on the other hand, acts along the surface. If the object is moving, friction acts opposite to the direction of motion, giving it a component in the direction opposite to displacement. That results in negative work by friction (it reduces the object's kinetic energy). More generally, any force that has a component in the direction of motion will do work (positive if it points forward with the motion, negative if it points backward).

So the statement that captures the general rule—forces with a component in the direction of motion do work—is the correct one. Gravity and the normal do no work here, while friction does work (negatively) when there is motion.