CalculateY
Quick Answer
A 100 N force moving an object 5 m does 500 J of work. At 60 degrees, the same force and distance produce 250 J. Power equals work divided by time: 500 J in 10 seconds = 50 watts.
Work (W = Fd cos θ)
Angle between force and displacement. 0° = force parallel to motion, 90° = no work done.
Power (P = W/t)
Common Examples
| Input | Result |
|---|---|
| F = 100 N, d = 5 m, θ = 0° | W = 500 J |
| F = 100 N, d = 5 m, θ = 60° | W = 250 J |
| W = 1,000 J, d = 10 m, θ = 0° | F = 100 N |
| W = 500 J, F = 50 N, θ = 0° | d = 10 m |
| W = 500 J, t = 10 s | P = 50 W |
How It Works
This calculator uses the work-energy theorem definition of mechanical work:
\[W = F \cdot d \cdot \cos(\theta)\]Where:
- W = work in joules (J)
- F = force in newtons (N)
- d = displacement in meters (m)
- θ = angle between the force vector and the direction of displacement
Effect of angle
When θ = 0°, cos(0°) = 1, so W = Fd. The full force contributes to work because force and motion point in the same direction. This is the maximum work a given force can do over a given distance.
When θ = 90°, cos(90°) = 0, so W = 0. A force perpendicular to motion does no work. Carrying a box horizontally at constant height is one example: the upward support force is perpendicular to horizontal displacement, so no work is done by the carrier against gravity in the direction of travel.
When θ > 90°, the cosine is negative, so work is negative. This means the force opposes the displacement. Friction is a common example: it acts opposite to motion, so it does negative work on a sliding object.
Power
Power is the rate at which work is done:
\[P = \frac{W}{t}\]Where t is time in seconds and P is power in watts (W). One watt equals one joule per second. Kilowatts (kW) are common for larger systems: 1 kW = 1,000 W.
Worked example
Lifting a 20 kg box 3 meters vertically requires an upward force equal to the weight of the box: F = 20 × 9.81 = 196.2 N. The displacement is 3 m upward, parallel to the force, so θ = 0°.
W = 196.2 × 3 × cos(0°) = 588.6 J
If the lift takes 5 seconds, the average power is:
P = 588.6 / 5 = 117.7 W
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