Work and Power
Basics
Work done
\(\(W=Fx\)\)
(Work = Force \(\times\) distance travelled)
(Joules are measured in Newton Metres \(Nm^{-1}\))
What is the work done when pushing a box weighing 40N over a distance of 2m?
- \(W=Fx\)
- \(40N\times2m=80J\)
What is the work done when a phone weighing 150g falls 1m.
- \(W=Fx\)
- \(F=0.15N\)
- \(1.5N\times 1m=1.5J\)
An object is being moved up a smooth slope up to a height of 0.5m. The weight of the ball is 8N. How much work is done?
- Since work is only done against the direction of gravity, the same work is done no matter the distance it took to get there.
- \(W=Fx\)
- \(8\times 0.5=4J\)
Angles
Work done at an angle to motion
- Some questions will involve a force that is at an angle to the direction of travel.
- In this case we resolve the force with the angle to the dirction of motion.
- If something is moving horizontally then we can use \(W=F x\times \cos\theta\)
Power
Equation for Power
\[P=Fv$$
$$P=\frac{W}{t}$$
$$P=\frac{Fs}{t}\]
Equation for power at an angle
\[P=Fv\times \cos\theta\]
Example
Q1
\(W=Fx\)
- Distance: \(2.81\)
- Force: \(203\)
- Work: \(570.43\)
Q2
\(W=F x\times \cos\theta\)
- Distance: \(1.39\)m
- Angle: \(\cos(13.1^\circ)\)
- Force: \(371\)N
- Work: \(502.27\)
Q3
\(P=Fv\)
- Power: \(60100\)W
- Velocity: \(34.7\)m/s
- Force: \(1732\)N
Q4
- Area under the graph: \(103,125J\)