Work, energy and power: study guide

Key ideas

Energy methods avoid following forces moment by moment. The work done by the net force equals the change in kinetic energy, and when only conservative forces act, the total mechanical energy stays constant.

• Work is W = Fd cos θ, where θ is the angle between the force and the displacement. A force perpendicular to the motion does no work.
• Kinetic energy is ½mv², gravitational potential energy near Earth is mgh, and a spring stores ½kx².
• Power is the rate of doing work: P = W ÷ t, or P = Fv for a force along the velocity.
• Friction and other non-conservative forces take mechanical energy out of the system as heat, so include their work in the balance.

Key equations

• W = Fd cos θ
• KE = ½mv²
• PE = mgh
• PE = ½kx²
• P = W ÷ t = Fv
• W_net = ΔKE

Worked example

A 2.0 kg ball is dropped from 5.0 m (g = 9.8 m/s²). The potential energy lost is mgh = 2.0 × 9.8 × 5.0 = 98 J, and it becomes kinetic energy. Setting ½mv² = 98 J gives v = √(2 × 98 ÷ 2.0) = 9.9 m/s. The mass cancels, so v = √(2gh) for any ball.

Common mistakes

• Using the whole force in W = Fd when the force is at an angle to the displacement.
• Forgetting that kinetic energy depends on the square of the speed: doubling the speed quadruples the energy.
• Mixing up energy, measured in joules, with power, measured in watts.

Practice

Test yourself with practice questions on this topic: Work, energy and power