Conservation of EnergyConservation of Energy

►EnergyEnergy WorkWork

►Kinetic and Potential EnergyKinetic and Potential Energy Conservative and non-conservative forcesConservative and non-conservative forces Other forms of energyOther forms of energy

IntroductionIntroduction

►Forms of energyForms of energy Mechanical energyMechanical energy

►Focus for nowFocus for now

►Forms of energyForms of energy Energy can be transformed from one form Energy can be transformed from one form

to anotherto another►Essential to the study of physics, chemistry, Essential to the study of physics, chemistry,

biology, geology, astronomybiology, geology, astronomy Can be used in place of Newton’s law to Can be used in place of Newton’s law to

solved certain problems more easily. solved certain problems more easily.

WorkWork►Provides a link between force and energyProvides a link between force and energy►Work is the product of the component of Work is the product of the component of

the force along the direction of the the force along the direction of the displacement and the magnitude of the displacement and the magnitude of the displacementdisplacement W=F(cosW=F(cos)d)d

–F(cos) is the component of the force in the direction of the displacement

–d is the displacement

WorkWork

►This gives no information aboutThis gives no information about The time it took for the displacement to The time it took for the displacement to

occuroccur The velocity of acceleration of the objectThe velocity of acceleration of the object

►Note: work is zero whenNote: work is zero when There is no displacement (holding a bucket)There is no displacement (holding a bucket) Force and displacement are perpendicular Force and displacement are perpendicular

to each other (if we are carrying the bucket to each other (if we are carrying the bucket

horizontally, gravity does not work)horizontally, gravity does not work)

http://lectureonline.cl.msu.edu/~mmp/kap5/work/work.htm

More about WorkMore about Work► Work is a scalar quantityWork is a scalar quantity► Units of work are Nm or Joules (J)Units of work are Nm or Joules (J)► Work can be positive or negativeWork can be positive or negative

Positive if the force and the Positive if the force and the displacement are in the same displacement are in the same directiondirection

Negative if the force and the Negative if the force and the displacement are in the opposite displacement are in the opposite directiondirection

► Example lifting a cement blockExample lifting a cement block Work done by the personWork done by the person

► Is positive when lifting the boxIs positive when lifting the box► Is negative when lowering the boxIs negative when lowering the box

Examples of Work Examples of Work CalculationsCalculations

W=F(cosW=F(cos)d)dSince there is Since there is

no angleno angleW=FdW=Fd=(100N)5m=(100N)5m= 500J= 500J

W=F(cosW=F(cos)d)d=(100N)=(100N)(cos30)5m(cos30)5m= 433J= 433J

W=F(cosW=F(cos)d)dSince the force required Since the force required to lift up is equal and to lift up is equal and opposite to gravity then opposite to gravity then F=+mg F=+mg sosoW=+mgdW=+mgdW=(15kg)(9.81m/W=(15kg)(9.81m/ss22)5m)5mW= 735JW= 735J

Example 4Example 4► A 10-N forces is applied A 10-N forces is applied

to push a block across to push a block across a friction free surface a friction free surface for a displacement of for a displacement of 5.0 m to the right. 5.0 m to the right.

Since Fapp is the only horizontal force, it is the only force that does work

•W = Fd• = (10N)(5.0m)• = 50J

Example 5Example 5► A 10-N force is A 10-N force is

applied to push applied to push a block across a a block across a frictional surface frictional surface at constant at constant speed for a speed for a displacement of displacement of 5.0 m to the 5.0 m to the right right

Since the object moves horizontally, only horizontally forces will do workWapp = FappdW = 10N 5.0 m = 50 JWfrct = Ff d = -10N(5.0 m) = -50J

Graphing WorkGraphing Work► A graph of force exerted over a displacement can be used to A graph of force exerted over a displacement can be used to

determine work. Since Work = Force x displacement and determine work. Since Work = Force x displacement and Area = length x width. If the axes on a graph are force and Area = length x width. If the axes on a graph are force and distance then the area under the line will be equivalent to distance then the area under the line will be equivalent to work done.work done.

Find the work done over the 10 m displacement.Area = work, there are 3 distinct areas under the line the sum will equal total work done.Area = ½ bh + lw + ½ bh = ½ 3m(20N) + 5m(20N) + ½ 2m (20N) = 30 J + 100 J + 20 J = 150JWork done is 150 J

Assignment 1Assignment 1

►Do questions 1 – 7 in workbookDo questions 1 – 7 in workbook