In physics, “work” differs from its everyday meaning. When a force moves an object, the product of the force and displacement is work.
Basic Knowledge
Work W is defined when a force F moves an object through a displacement x:W = F cos θ × x = Fx cos θ
θ is the angle between the directions of the force and displacement.
When the force and direction of motion are the same(θ=0): W = Fx(maximum)
When the force and direction of motion are perpendicular(θ=90°): W = 0(no work is done)
When the force and direction of motion are opposite(θ=180°): W = -Fx(negative work)
The unit is J (joule). 1 J = 1 N·m.
Power P = work ÷ time = W/t
The unit is W (watt). 1 W = 1 J/s.
Power can also be expressed as P = Fv using velocity v(when the force and velocity are in the same direction).
Work W (work)（Force × displacement × cos θ. Unit: J）
Power P (power)（Work done per unit time. W/t or Fv. Unit: W）
Joule (J)（Unit of work and energy. 1 J = 1 N·m）
Watt (W)（Unit of power. 1 W = 1 J/s）
Positive work and negative work（Cases in which a force assists or hinders motion）
Work when θ = 90° = 0（A perpendicular force does no work）
Further Study (Background and Significance)
Simply holding a heavy load while standing still involves 0 physical work. Even if a force is applied, if there is no displacement, W = F×0 = 0 J. This differs greatly from the everyday meaning of “work.”
It is also important that “a perpendicular force does no work.” In uniform circular motion, centripetal force is always perpendicular to velocity(the direction of motion), so centripetal force does no work.
Power indicates “how quickly the same amount of work can be done.” Horsepower(hp) is also a unit of power, and 1 hp ≈ 746 W. Electrical power is a type of power, which is why the power consumption of household electrical devices is expressed in “W(watts).”
Negative work occurs when a force hinders motion. Friction and air resistance always do negative work on an object, changing kinetic energy into thermal energy.
- W = Fx cos θ(θ is the angle between the force and displacement)
- θ=0: W=Fx(maximum), θ=90°: W=0, θ=180°: W=-Fx
- Unit: J(joule) = N·m
- Power P = W/t = Fv, unit: W(watt)
- Without displacement, work is 0
- A perpendicular force does no work
- Negative work = the force is hindering motion
Points to Note (Common Confusions)
① Without displacement, work is 0. Applying a force without moving the object means no work is done. ② θ is the angle between the force and displacement, and cos θ must be used when the directions differ, such as an upward diagonal force acting during horizontal displacement. ③ Do not confuse the units of work(J) and power(W). “Watt” is the unit of power. ④ The formula P = Fv holds only when the force and velocity are in the same direction.
Practice
- An object was pushed horizontally through 5 m by a force of 30 N. Find the work done.
- An object was lifted by a force of 60 N while moving horizontally through 3 m. If the angle between the force and displacement is 90°, how much work was done?
- A work of 600 J was done in 20 seconds. Find the power(W).