Work, Energy and Power

When an object moves under the influence of a force, then work is done according to the equation 8.1 <math display='block'> <mrow> <mi>W</mi><mo>=</mo><mi>F</mi><mo>&#x00D7;</mo><mi>s</mi> </mrow> </math>$$W = F \times s$$ where W is the work done, F is the force (N) and s is the displacement (m) in the direction of the force. The SI unit of work is the joule (J), which is a scalar quantity defined as the work done when the point of application of a force of 1 N moves 1 m in the direction along which it is being applied. If the force is applied at an angle to the displacement, as in Figure 8.1, then we must use the magnitude of its component in the displacement direction, in which case Equation (8.1) becomes 8.2 <math display='block'> <mrow> <mi>W</mi><mo>=</mo><mi>F</mi><mi>cos</mi><mi>&#x03B8;</mi><mo>&#x00D7;</mo><mi>s</mi> </mrow> </math>$$W = F\cos \theta \times s$$ where θ is the angle which the force makes with the displacement. If θ = 0°, then cos θ = 1 and we have Equation (8.1). If θ = 90°, cos θ = 0, so the force has no component and can do no work in the displacement direction.