Work Energy Theorem

# Overview

Work is defined as the amount of force required to change the energy of a system. Therefore, work is defined as "transferred energy" and doing work is defined as the act of transferring the energy. The work energy theorem states that the change in energy of a system is equal to the work done by the surroundings.

# Equations

## Equation One

W = Fr*cos(theta) - (AP Physics Equation Sheet)
W = work, F = net force, r = distance

## Equation Two

Final Energy = Initial Energy + Work
These initial and final energies include all types of energy (Potential, Kinetic, Ect.)

A 55 kg gymnast lands with a vertical velocity of -6.6 m/s, she applies a force over a distance or height of -.4 m to reduce her velocity to -1.1 m/s. How much work did she do during this landing?

An 70 kg diver is jumping on the diving board. Position (a) is the point of maximum depression of the board, the diver has a vertical velocity of -1.5 m/s and a height of 1.8 m. Position (b) is the point of takeoff from the diving board, the diver has a height of 2.5 m and a vertical velocity of 3.0 m/s. Find the work done from (a) to (b).

# Special Cases

In a single dimension, the work done is equal to the Force in that direction times the distance. In two dimensions, it is equal to the force in the x direction times distance in the x direction + distance in the y direction times distance in the y direction. This also holds true for three dimensions and the z direction.

# Applications

• Work and energy can be used to solve many kinematics type problems without getting into position and acceleration. Most allow problems to be solved using simply mass, velocity, and a distance.