Work done
Equations
-
\[1J=1Nm\]
The force \(Y\)N moves a particle, mass \(m\)kg, \(x\)m up a rough slope inclined at \(30^{\circ}\) to the horizontal.
- \(\text{work done}=\Delta gpe\)
- Some of this work is done against friction (transferred to heat): \(F_{r}x\)
- Some of this work is done against gravity: \(=x\times mg\sin(30)\)
A package of mass 2kg is pulled at a constant speed up a rough plane which is inclined at \(30^{\circ}\) to the horizontal. The coefficient of friction is \(0.35\). The package is drawn 12m up the slope.
- Angle: \(30^{\circ}\)
- Weight: \(2g (2\times9.81)\)
- Work done against gravity = \(2g\times \sin30\times12=g\times12=12g\)
- Work done against friction \(= \mu \times R\) where \(\mu\) is the coefficient of friction
- \(R-2g\cos30\) because forces must be equal
- Therefore \(R=\sqrt{ 3 }g\) N
- Work done against friction: \(=\sqrt{ 3 }g\times0.35\)
- Total work done by the pulling force: \((\sqrt{ 3 }g\times0.35)+12g\) (work done against both of the above added together)