Work and Energy Summary Sheet Chapter 6

Work: work is done when a force is applied to a mass through a displacement or W=Fd. The force and the displacement must be parallel to one another in order for work to be done. F (N)

W =(Fcosθ)d F If the force is not parallel to The area of a force vs. the displacement, then the displacement graph + W component of the force that represents the work θ d (m) is parallel must be found. done by the varying - W d force.

Signs and Units for Work Work is a scalar but it can be positive or negative. Units of Work

F d W = + (Ex: pitcher throwing ball) 1 N•m = 1 J (Joule)

F d W = - (Ex. catcher catching ball) Note: N = kg m/s2 •

Work – Energy Principle Hooke’s Law x The work done on an object is equal to its change F = kx in kinetic energy. F F is the applied force. 2 2 x W = ΔEk = ½ mvf – ½ mvi x is the change in length. k is the spring constant. F

Energy Defined Units Energy is the ability to do work. Same as work: 1 N•m = 1 J (Joule)

Kinetic Energy Potential Energy Potential energy is stored energy due to a system’s shape, position, or Kinetic energy is the energy of state. motion. If a mass has velocity, Gravitational PE Elastic (Spring) PE then it has KE 2 Mass with height Stretch/compress elastic material E = ½ mv k 2 EG = mgh EE = ½ kx To measure the change in KE use: Change in EG Change in ES 2 2 2 2 ΔEk = ½ mvf – ½ mvi ΔEG = mghf – mghi ΔEE = ½ kxf – ½ kxi

Conservation of Energy “The total energy is neither increased nor decreased in any process. Energy can be transferred from one object to another and transformed from one form to another, but the total energy remains constant.”

WD = ΔEk + ΔEG + ΔEE

W is the work done by dissipative forces (friction, air resistance; any force that transforms energy in such a D way that it can not be given back). IF no dissipative forces are present, then W = 0. D Questions to ask when setting up the equation: Other Problem Solving Tips . Does the mass’s velocity change? . Draw a p icture and label it . Does the mass’s height change? . Label/list initial and final conditions . Is an elastic material (spring) involved? . List what you need to find . Are any dissipative forces acting? Power Power is: Units of measure: The equation . the rate at which work is done Watt (W) or horse power (hp) P = Work/time = W/t . the rate at which energy is transferred

1J/s = W (metric) Energy transferred? Variations: 746 W = 1 hp (English) Light bulb electrical energy to light energy P = W/t = Fd/t = Fv Car engine chemical energy to mechanical energy