3Definition of WorkIn Physics, work means more than something that requires physical or mental effortWork is done on an object when a force causes a displacement of the objectWork is the product of the force applied to an object and the displacement of the object
4Caution!Work is done only when a force or a component of a force is parallel to a displacement!
6Units of Work The SI unit of work is the joule (J) Derived from the formula for workThe joule is the unit of energy, thus….Work is a type of energy transfer!!
7Sample Problem AHow much work is done on a sled pulled 4.00 m to the right by a force of 75.0 N at an angle of 35.0° above the horizontal?FFd cosθθd
8How much work was done by Fg on the sled? FNFupFFyFxθFkdHow much work was done by Fg on the sled?How much work was done by Fup on the sled?If the force of kinetic friction was 20.0 N, how much work was done by friction on the sled?Fg
9The Sign of WorkWork is a scalar quantity and can be positive or negativeWork is positive when the component force & displacement have the same directionWork is negative when they have opposite directions
10FFupθFkdFgIf the force of kinetic friction was 20.0 N, how much work was done by friction on the sled?Wf = Fk∙d = (-20.0 N)(4.00 m) = J
11Graphical Representation of Work Work can be found by analyzing a plot of force and displacementThe product F∙d is the area underneath and Fd graph
12Graphical Representation of Work This is particularly useful when force is not constant (which it normally isn’t)
18Importance of W-KE Theorem Some problems that can be solved using Newton’s Laws turn out to be very difficult in practiceVery often they are solved more simply using a different approach…An energy approach.
19Sample Problem CA 10.0 kg sled is pushed across a frozen pond such that its initial velocity is 2.2 m/s. If the coefficient of kinetic friction between the sled and the ice is 0.10, how far does the sled travel? (Only consider the sled as it is already in motion.)viFNFkmgd
21Potential Energy PE is “stored” energy It has the “potential” to do workEnergy associated with an object due to its positionGravitational PEgDue to position relative to earthElastic PEeDue to stretch or compression of a spring
22Two Types of Potential Energy ElasticGravitationalPEe = ½ kx2PEg = mgh
23Gravitational Potential Energy Gravitational PE is energy related to positionPEg = mghGravitational PE is relative to positionZero PE is defined by the problemIf PEc is zero, then PEA > PEB > PEC
24Elastic Potential Energy PE resulting from the compression or stretching of an elastic material or spring.PEe = ½ kx2 where…x = distance compressed or stretchedk = spring constantSpring constant indicates resistance to stretch.
255.3 Conservation of Energy Objectives At the end of this section you should be able toIdentify situations in which conservation of mechanical energy is validRecognize the forms that conserved energy can takeSolve problems using conservation of mechanical energy
26Conserved QuantitiesFor conserved quantities, the total remains constant, but the form may changeExample: one dollar may be changed, but its quantity remains the same.Example: a crystal of salt might be ground to a powder, but the mass remains the same. Mass in conserved
27Mechanical Energy Is conserved in the absence of friction MEi = MEf i.e. initial ME equals final MEMEi = MEfIf ME = KE + PEThen KEi + PEi = KEf + PEf½ mvi2 + mghi = ½ mvf2 + mghf
28Conservation of Mechanical Energy ( A Falling Egg) Time (s)Hght (m)Spd (m/s)PE(J)KEME0.001.000.740.100.950.980.700.040.200.802.000.590.150.300.562.900.410.330.400.223.900.160.580.454.43As a body falls, potential energy is converted to kinetic energySince ME is conserved (constant)…. ΣPE + KE = MEIn the absence of friction & air resistance, this is true for mechanical devices also
29Mechanical Energy Is the sum of KE and all forms of PE in the system ME = ΣKE + ΣPEsigma (Σ ) indicates “the sum of”
30Sample Problem 5EStarting from rest, a child of 25.0 kg slides from a height of 3.0 m down a frictionless slide. What is her velocity at the bottom of the slide?Could solve using kinematic equations, but it is simpler to solve as energy conservation problem.MEi = MEf
31ME may not be conservedIn the presence of friction, mechanical energy is not conservedFriction converts some ME into heat energyTotal energy is conservedMEi = MEf + heat
32Work-Kinetic Energy Theorem The net work done on an object is equal to the change in kinetic energy of the objectWnet = ∆KEThe work done by friction is equal to the change in mechanical energyWfriction = ∆ME
33Power Is the rate of work, the rate at which energy is transferred P = W/∆tSince W = Fd, P = Fd /∆t orP = FvavgUnit of power = the watt (W)1 W = 1 J/s1 hp = 746W horsepower