MCAT Physics > Energy

## Background

**Energy (E)** is the capacity of a physical substance to do work (scalar value)

## Potential Energy

**Potential Energy (PE/U)** is the energy that has the potential to do something

PE (U) = mgh

## Kinetic Energy

**Kinetic Energy (KE)** is the energy of motion

KE = ½mv^{2}

## Mechanical Energy

**Total Mechanical Energy** is the sum of kinetic and potential energy

ΔE_{total} = ΔPE (U) + ΔKE

**Conservation of Mechanical Energy** states in the absence of non-conservative forces, the sum of the KE and PE will be constant. If work done to move a particle is zero, or the net forces is the same, then force is conservative. When non-conservative forces are present (friction/air resistance) energy is not fully conserved and some is lost to heat, sound or other factors. To increase available kinetic energy, increase potential energy

½mv^{2} = mgh = 0

## Work

**Work (W)** is the process by which energy is transferred between systems

W = Fd = Fdcosθ = KE = ½mv^{2} = PE = mgh

**Work/Energy Theorem** describes a direct relationship between the work done by all forces acting on an object and the change in the objects kinetic energy.

W_{net} = ΔKE

### Power

**Power (P)** is the rate at which energy (work) is transferred between systems

P = ΔW/Δt

### Momentum

**Momentum (p)** is a vector quantity of objects in motion (magnitude/direction of force). Momentum is conserved with constant net forces or in the absence of external forces

Σp = Σmv

### Impulse

**Impulse (J)** occurs when net forces act on an object causing it to change motion

J = Ft = Δp

### Efficiency

**Efficiency** is a comparison of the work put in and the work put out

Efficiency = AMA/TMA = W_{out}/W_{in} = ((load)(load distance))/(load)(load distance) x 100

## Collisions

**Ideal Collisions** occur when two objects instantaneously collide in a specific location and total momentum is conserved as long as no net forces act on the objects

1) **Completely Elastic Collisions** occur when 2+ objects collide such that the total momentum and KE are conserved. No energy has transformed into light, sound, etc.

mv_{ai} + mv_{bi} = mv_{af} + mv_{bf}

KE_{a1} + KE_{b1} = KE_{a2} + KE_{b2}

2) **Inelastic Collisions** occur when objects do not stick together and KE is converted to heat, light, sound, and object deformation. Doesn't result in a decrease of kinetic energy unless external forces are present (conservation)

mv_{ai} + mv_{bi} = mv_{af} + mv_{bf}

3) **Completely Inelastic Collisions** occur 2+ objects stick together and the kinetic energy is not conserved but momentum is

mv_{ai} + mv_{bi} = (m_{a} + m_{b})v_{f}

## Simple Machines

See Simple Machines

## Center of Mass

**Center of Mass** is a point within any 2D/3D object at which the entire objects mass could be represented by a single particle

Center of Mass (x,y,z…) = (m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3})/(m_{1} + m_{2} + m_{3})