Work, energy and power

Section FM1-2

1 spec leaf

Notes and three levels of exam-style practice for each registered specification leaf in this section.

Open the printable pack

FM1-2.1

Kinetic and potential energy, work and power. The work-energy principle. The principle of conservation of mechanical energy.

Kinetic energy is $\tfrac12mv^2$ , gravitational potential energy changes by $mg\Delta h$ , and work is $\int F\,dx$ when force varies with position.
The work-energy principle states that the work done by the resultant force equals the change in kinetic energy.
Mechanical energy is conserved when only conservative forces do work; resistance or driving forces must instead be included through their work.
Power is the rate of doing work: $P=dW/dt=Fv$ when the force and velocity are parallel. Do not use $P=Fv$ with an un-resolved force component.

Tier 1 · Easy

2 marks

ORIGINAL

A $1200\,\text{kg}$ car increases its speed from $10\,\text{m s}^{-1}$ to $14\,\text{m s}^{-1}$ . Calculate the net work done on the car.

Tier 2 · Standard

4 marks

ORIGINAL

A $1200\,\text{kg}$ car climbs a road inclined at $5^\circ$ to the horizontal at a constant speed of $20\,\text{m s}^{-1}$ . The resistance is $400\,\text{N}$ . Taking $g=9.8\,\text{m s}^{-2}$ , find the engine power.

Tier 3 · Hard

5 marks

ORIGINAL

A $2\,\text{kg}$ particle moves along a horizontal line. A constant driving force of $20\,\text{N}$ acts forwards while the resistance after displacement $x\,\text{m}$ is $(2+0.5x)\,\text{N}$ . Its speed at $x=0$ is $3\,\text{m s}^{-1}$ . Find its speed when $x=8$ .