UnofficialAP Physics 1Unit 3 of 8

AP Physics 1 Unit 3: Work, Energy and Power

Work-energy theorem, conservation of energy and power.

Unit overview

Energy methods are often faster than forces because energy is a scalar. Work done by a constant force is $W = Fd\cos\theta$ , and the work-energy theorem says the net work on an object equals its change in kinetic energy, $\Delta K = \tfrac{1}{2}mv_f^2 - \tfrac{1}{2}mv_i^2$ .

For a system with only conservative internal forces, mechanical energy $K + U$ stays constant, with $U_g = mgh$ near Earth and $U_s = \tfrac{1}{2}kx^2$ for springs. Friction transfers mechanical energy into internal energy, and external work changes the system's total energy. Power is the rate of energy transfer, $P = W/t$ or $P = Fv$ .

Key topics

Work: Only the component of force along the displacement does work; perpendicular forces do none.
Kinetic and potential energy: $K = \tfrac{1}{2}mv^2$ , $U_g = mgh$ , $U_s = \tfrac{1}{2}kx^2$ .
Conservation of energy: Choose a system, list energy forms at two instants and account for external work.
Power: Average power $W/t$ ; instantaneous power $Fv$ .

Worked example

A 2 kg ball is dropped from rest from a height of 5 m. Ignoring air resistance and taking $g = 10$ m/s², find its speed just before it lands.

$mgh = \tfrac{1}{2}mv^2$ , so $v = \sqrt{2gh}$ .
$v = \sqrt{2 \cdot 10 \cdot 5} = \sqrt{100}$ .
$v = 10$ m/s.

Answer: $v = 10$ m/s

Common mistakes

Forgetting that the normal force does no work when it is perpendicular to motion.
Using conservation of mechanical energy when friction acts on the system.
Mixing up the system: gravitational potential energy belongs to the object-Earth system.

Exam tips

Energy bar charts are a quick way to organise a justification; draw them if the question allows.
Mass often cancels in free-fall energy problems, which is a useful check on algebra.

See the AP Physics 1 exam format and every unit on the course page.