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Work done by a constant force
Beginner
Force component along displacement times displacement.
W = Fd cosθWork is energy transferred by a force over a displacement: W = Fd cosθ, where θ is the angle between force and displacement. Only the component along the motion does work.
Pulling a sled 10 m with 50 N at 30°: W = 50·10·0.866 = 433 J.
Carrying a bag horizontally at constant speed: the force (up) is perpendicular to the motion, so work is zero.
In more detail
Work is done when a force moves an object through a displacement, W = Fd cos θ, where θ is the angle between the force and the displacement. Only the component of force along the motion does work.
Real-world uses
- Lifting a crate to a shelf does work against gravity.
- Engine power ratings describe how fast an engine can do work on a vehicle.
- Lifting a shopping bag does work on it, while carrying the same bag along a flat corridor does no work against gravity.
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Frequently asked questions
Does a force perpendicular to motion do work?
No. A force at right angles to displacement, such as the tension in a swinging pendulum, does no work.
What are the units of work?
Joules, equal to newton metres.
Why does carrying a heavy bag horizontally feel tiring if no work is done?
Your muscles do internal work to hold the load steady, and that energy is used even though the bag's energy does not change.
Related topics in Work, Energy & Power
Units of work and energy · Positive, negative and zero work · Work from a force–displacement graph