Work, Energy, and Power Review

A comprehensive vocabulary review of core physics concepts involving work, energy forms, conservation laws, and standard numerical applications.

Kinetic Energy

The energy an object possesses due to its motion, defined mathematically by the equation $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

Potential Energy

The stored energy of an object resulting from its position, state, or configuration, with gravitational potential energy given by the equation $PE = mgh$, where $m$ is mass, $g$ is gravitational acceleration, and $h$ is height.

Work-Energy Theorem

A fundamental physics theorem stating that the net work done on an object is equal to the change in its kinetic energy: $W_{\text{net}} = \Delta KE$.

Total Energy in a Closed System

The total energy in a closed, isolated system remains constant over time; energy cannot be created or destroyed, only transformed from one form into another.

Kinetic Energy of a $3\,\text{kg}$ Ball Moving at $4\,\text{m/s}$

Calculated using the kinetic energy formula $KE = \frac{1}{2}mv^2 = \frac{1}{2}(3\,\text{kg})(4\,\text{m/s})^2 = 24\,\text{J}$.

Potential Energy of a $2\,\text{kg}$ Object at a Height of $6\,\text{m}$

Calculated using the gravitational potential energy formula $PE = mgh = (2\,\text{kg})(9.8\,\text{m/s}^2)(6\,\text{m}) = 117.6\,\text{J}$.

Kinetic Energy Dependence on Speed

Because kinetic energy is directly proportional to the square of speed ($KE \propto v^2$), doubling the speed of an object increases its kinetic energy by a factor of four ($4\times$).

Energy Transformation in a Swinging Pendulum

As a pendulum moves from its highest point to its lowest point, all of its gravitational potential energy is converted into kinetic energy, reaching maximum speed at the bottom.

Kinetic Energy from a Released $40\,\text{J}$ Stretched Spring

By conservation of mechanical energy ignoring friction, all $40\,\text{J}$ of stored elastic potential energy converts into kinetic energy, giving the attached mass $40\,\text{J}$ of kinetic energy upon release.

Velocity of an Object Falling $20\,\text{m}$ from Rest

Determined via conservation of energy ($v = \sqrt{2gh}$), yielding $v = \sqrt{2(10\,\text{m/s}^2)(20\,\text{m})} = \sqrt{400} = 20\,\text{m/s}$ just before impact.

Work Done by a $50\,\text{N}$ Force Over $3\,\text{m}$

Calculated using the formula $W = Fd = (50\,\text{N})(3\,\text{m}) = 150\,\text{J}$.

Work Done by a $20\,\text{N}$ Force Over $4\,\text{m}$

Calculated using the work formula $W = Fd = (20\,\text{N})(4\,\text{m}) = 80\,\text{J}$ (the object's mass is not required when the net applied force is provided).

Energy Transformation in a Hydroelectric Plant

Gravitational potential energy of elevated water converts to kinetic energy as it falls, turns turbines to produce mechanical energy, and is finally converted into electrical energy by a generator.

Energy Conservation During Braking

The kinetic energy of the moving vehicle is transformed via friction between brake pads and wheels primarily into thermal energy (heat) and sound, conserving total energy.

Speed of a Diver Falling from $10\,\text{m}$

Calculated using $v = \sqrt{2gh} = \sqrt{2(10\,\text{m/s}^2)(10\,\text{m})} = \sqrt{200}\,\text{m/s} \approx 14.14\,\text{m/s}$ just prior to water entry.

Work Done by a $100\,\text{N}$ Force Over $5\,\text{m}$

Calculated using the work relationship $W = Fd = (100\,\text{N})(5\,\text{m}) = 500\,\text{J}$.

Mechanical Energy

The total energy of an object associated with its motion and position, defined as the sum of kinetic energy ($KE$) and potential energy ($PE$): $ME = KE + PE$.

Potential Energy Gain from Lifting Work

When $250\,\text{J}$ of work is done against gravity to lift an object, the potential energy gained by the object is exactly equal to the work done: $\Delta PE = 250\,\text{J}$.

Kinetic Energy with Frictional Dissipation on a Ramp

Calculated by subtracting energy lost to friction from the initial potential energy: $KE_{\text{bottom}} = PE_{\text{initial}} - W_{\text{friction}} = 200\,\text{J} - 20\,\text{J} = 180\,\text{J}$.

Work-Force-Displacement Formula

The mathematical relation $W = Fd\cos(\theta)$, where $W$ is work in Joules ($\text{J}$), $F$ is the magnitude of the applied force in Newtons ($\text{N}$), $d$ is displacement in meters ($\text{m}$), and $\theta$ is the angle between the force and displacement vectors.