Work, Energy, and Power

Five topics on energy as a bookkeeping shortcut around Newton's second law. The kinetic energy a moving object carries, the work a force does as the integral $W = \int \vec{F} \cdot d\vec{r}$ and how net work sets $\Delta K$, the potential energy a conservative force stores with $\vec{F} = -\dfrac{dU}{dx}$, the conservation of the running total $K + U$ when nothing dissipative acts, and finally power, the instantaneous rate $\dfrac{dW}{dt}$ at which energy moves.

Topics

3.1

Translational Kinetic Energy

Work and the Work-Energy Theorem

Potential Energy

Conservation of Energy

Power

Lesson

Diag

locked

Equations For every problem in this unit

Kinetic energy

$K = \tfrac{1}{2}mv^2$

Work-energy theorem

$W_{net} = \Delta K$

Gravitational PE, near Earth

$\Delta U_g = mg\,\Delta y$

Elastic potential energy

$U_s = \tfrac{1}{2}k(\Delta x)^2$

Work, constant force

$W = Fd\cos\theta$

Work, variable force

$W = \int \vec{F} \cdot d\vec{r}$

Average power

$P_{avg} = \dfrac{W}{\Delta t}$

Instantaneous power

$P = \vec{F} \cdot \vec{v} = \dfrac{dW}{dt}$

Mechanical energy

$E = K + U$

Conservation, isolated system

$\Delta K + \Delta U = 0$

Force from potential energy

$\vec{F} = -\dfrac{dU}{dx}$

With nonconservative work

$W_{nc} = \Delta K + \Delta U$

Unit 3 tools

Challenge bank

1 / 30

30 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items pulled from across all 5 topics. Identifies which misconceptions still bite when you cannot see which topic the question came from.