Work, Energy & Power Formulas
Complete reference for mechanical work, kinetic/potential energy, and power ratings.
Constant Force Work
Work by Gravity
Variable Force Work
Work-Energy Theorem
Kinetic Energy
Gravitational PE
Elastic Potential Energy
Rotational Kinetic Energy
Average Power
Instantaneous Power
Efficiency
Electrical Power
The Currency of the Universe
In Physics, Energy is like money. You can have it in different forms (cash, bank, gold) representing Kinetic, Potential, or Thermal energy. Work is the act of spending or earning that money (transferring energy). Power is how fast you spend it.
Conservation of Energy
The most fundamental law: Energy cannot be created or destroyed, only transformed. If a ball falls, Potential Energy turns into Kinetic Energy. Total Energy stays the same.
$$ KE_i + PE_i = KE_f + PE_f $$
Rotational Energy
Moving in a circle takes energy too! A spinning flywheel stores energy just like a moving car. We simply swap Mass ($m$) for Moment of Inertia ($I$) and velocity ($v$) for angular velocity ($\omega$).
Work vs Power: What's the difference?
This is the most common confusion point.
"How much did you do?"
Lifting 100 bricks to the roof is a fixed amount of Work, whether it takes you 1 hour or 1 minute.
"How fast did you do it?"
Lifting those bricks in 1 minute requires huge Power. Lifting them in 1 hour requires low Power.
Variable Forces
Simple formulas like $W = Fd$ only work if Force is constant. If the force changes (like pulling a bowstring, where it gets harder as you pull), you must use Calculus or area under the graph.
"Work is the integral of Force over Distance."
Frequently Asked Questions
What is the Work-Energy Theorem?
It states that the Net Work done on an object is equal to the change in its Kinetic Energy ($W_{net} = \Delta KE$). This is a powerful tool because it links Forces (Work) directly to Speed (Kinetic Energy) without needing to know time or acceleration.
What is the difference between Kinetic and Potential Energy?
Kinetic Energy ($KE$) is the energy of MOTION. If it moves, it has KE. Potential Energy ($PE$) is STORED energy due to position or shape (like holding a ball high up or stretching a spring). PE can turn into KE.
Why is work zero if I push a wall?
Because Work = Force × Displacement ($W = Fd$). Even if you push with huge Force, if the Displacement ($d$) is zero, the Work is zero. You interpret your tiredness as "work", but physically, no energy was transferred to the wall.
What is a "Watt"?
A Watt is the unit of Power. 1 Watt = 1 Joule per second. It generally measures how fast you are using or generating energy. A 1000W microwave delivers energy 10 times faster than a 100W bulb.
Does friction do negative work?
Yes! Friction force usually points opposite to the direction of motion ($ heta = 180^{circ}$). Since $cos(180^{circ}) = -1$, the work done by friction is negative. This removes energy from the system (usually turning it into heat).
What is Hooke’s Law?
Hooke's Law ($F = -kx$) describes the force needed to extend or compress a spring. The Elastic Potential Energy stored in that spring is $U = 0.5kx^2$.
How does efficiency relate to power?
Efficiency ($eta$) is the ratio of Output Power to Input Power ($P_{out}/P_{in}$). No machine is 100% efficient due to energy lost as heat or sound. Real machines always require more input power than they produce in useful output.
What is "Conservative Force"?
A force is conservative if the work it does depends only on the start and end points, not the path taken. Gravity and Spring forces are conservative. Friction is NOT conservative (path matters).
Can Kinetic Energy be negative?
No. Since mass ($m$) is positive and velocity squared ($v^2$) is always positive, $KE = 0.5mv^2$ is always zero or positive. You cannot have "negative motion".
What is 1 kWh (Kilowatt-hour)?
It looks like a power unit, but it is actually a unit of ENERGY. $1 kWh$ is the energy used by a 1000W device running for 1 hour. It equals 3.6 million Joules.