Work-Energy Theorem Worked Examples Cheat Sheet

Key Facts

• The work-energy theorem is $W_{\text{net}} = \Delta K = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$.
• Work done by a constant force is $W = Fd\cos\theta$, where $\theta$ is the angle between the force and displacement.
• Kinetic energy is $K = \frac{1}{2}mv^2$, so speed affects kinetic energy by the square of $v$.
• Positive net work increases speed because $W_{\text{net}} > 0$ means $K_f > K_i$.
• Negative net work decreases speed because $W_{\text{net}} < 0$ means $K_f < K_i$.
• Gravitational potential energy near Earth's surface is $U_g = mgh$, where $h$ is height relative to a chosen zero level.
• Friction usually does negative work given by $W_f = -f_k d$ when it acts opposite the motion.
• With nonconservative work, energy can be tracked using $K_i + U_i + W_{\text{nc}} = K_f + U_f$.

Vocabulary

Work

Work is energy transferred by a force acting through a displacement, calculated for a constant force by $W = Fd\cos\theta$.

Net Work

Net work is the total work done by all forces on an object, written as $W_{\text{net}} = \sum W$.

Kinetic Energy

Kinetic energy is the energy of motion, calculated by $K = \frac{1}{2}mv^2$.

Work-Energy Theorem

The work-energy theorem states that the net work on an object equals its change in kinetic energy, $W_{\text{net}} = \Delta K$.

Conservative Force

A conservative force stores and returns energy, so its work can be represented by a change in potential energy.

Nonconservative Force

A nonconservative force, such as friction, changes mechanical energy by converting some energy to thermal energy or other forms.