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Work and Energy Dr. Robert MacKay Clark College

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Introduction What is Energy? What are some of the different forms of energy? Energy = $$$

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Overview Work (W) Kinetic Energy (K) Potential Energy (U) All Are measured in Units of Joules (J) 1.0 Joule = 1.0 N m W K U

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Overview Work Kinetic Energy Potential Energy W K U Heat Loss

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Work and Energy Work = Force x displacement W = F d Actually Work = Force x displacement parallel to force r =4.0 m F= 6.0 N W= F r = 6.0 N (4.0m) = 24.0 J

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Work and Energy Work = Force x Displacement parallel to force r = 8.0 m F= N W= F r = -6.0 N (8.0m) =-48 J

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Work and Energy Work = Force x Displacement parallel to force r = 6.0 m F= ? N W= 60 J

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Work and Energy Work = Force x Displacement parallel to force r = ? m F= N W= 200 J

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Work and Energy Work = Force x Displacement parallel to force r = 8.0 m F= N W= 0 (since F and d are perpendicular

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Fig. 7.2, p.184

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Work and Energy Work = F r Dot product W = F r cos (40) r = 8.0 m F= N 40° W= (6.0N) [8.0m cos(40) ]= 36.8 J

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Work and Energy Work = F r Dot product W = F r cos(40) r = 8.0 m F= N 40° W= (6.0N cos(40) ) [8.0m]= 36.8 J

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Fig. 7.7a, p.189 Total Area ~ A) Work ~ F x x) ~ ~

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Fig. 7.7b, p.189

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Work Variable Force ( =0) Work = F r cos = F avg x

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Springs 101 Spring Constant k, stiffness = 50 N/m

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Work Variable Force ( =0) Work = F D cos = F D

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Work Variable Force ( =0) Work = Area units of N m (Joules) W= 0.5*(100N)(4m) - 0.5(50N)2m) = +200 J -50 J = 150 J

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Potential Energy, U Gravitational Potential EnergyGravitational Potential Energy SpringsSprings ChemicalChemical PressurePressure Mass (Nuclear)Mass (Nuclear) Measured in JoulesMeasured in Joules

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Potential Energy, U Gravitational Potential EnergyGravitational Potential Energy SpringsSprings ChemicalChemical PressurePressure Mass (Nuclear)Mass (Nuclear) The energy required to put something in its place (state)

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Potential Energy Gravitational Potential Energy = weight x height U=(mg) h 4.0 m m = 2.0 kg

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Potential Energy U=(mg) h 4.0 m m = 2.0 kg K=? U=80 J

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Potential Energy to Kinetic Energy U=(mg) h 2.0 m m = 2.0 kg KE=? PE=40 J 1.0 m K E= 0 J

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Potential Energy of a spring U= 1 2 kx 2 x

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Potential Energy of a spring U= 1 2 kx 2 x For a spring with stiffness k= 80 N/m, what is its potential energy when stretched 0.1m? How about 0.2 m?

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Potential Energy of a spring = 1 2 kx 2 x For a spring with stiffness k= 80 N/m, what is its potential energy when stretched 0.1m? How about 0.2 m? U= N/m (0.1m) 2 = 0.40 J

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Potential Energy of a spring = 1 2 kx 2 x For a spring with stiffness k= 80 N/m, what is its potential energy when stretched 0.1m? How about 0.2 m? U= N/m (0.2m) 2 = 1.60 J

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Potential Energy of a spring U= 1 2 kx 2 x

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Table 7.1, p.194 Kinetic Energy K= 1 / 2 mv 2

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Kinetic Energy, K K =1/2 m v 2 m=2.0 kg and v= 5 m/s K= ?

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Kinetic Energy K =1/2 m v 2 m=2.0 kg and v= 5 m/s K= 25 J m=4.0 kg and v= 5 m/s K= ? m=2.0 kg and v= 10 m/s K= ?

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Kinetic Energy K =1/2 m v 2 if m doubles KE doubles if v doubles KE quadruples if v triples KE increases 9x if v quadruples KE increases ____ x

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Work Energy Theorm K =1/2 m v 2 F = m a

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Work Energy Theorm K =1/2 m v 2 F = m a F d = m a d

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Work Energy Theorm K =1/2 m v 2 F = m a F d =m a d F d = m (v/t) [(v/2)t]

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Work Energy Theorm K =1/2 m v 2 F = m a F d = m a d F d = m (v/t) [(v/2)t] W = 1/2 m v 2

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Work Energy Theorm KE =1/2 m v 2 F = m a F d = m a d F d = m (v/t) [(v/2)t] W = 1/2 m v 2 W = KE

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Work Energy Work Energy W = K How much work is required to stop a 2000 kg car traveling at 20 m/s (45 mph)?

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Work Energy Work Energy W = K How much work is required to stop a 2000 kg car traveling at 20 m/s (45 mph)? W= K =-1/2 m v 2 =-1/2(2000 kg)(20 m/s) 2 = kg (400 m 2 /s 2 ) = - 400,000 Joules

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Work Energy Work Energy W = K How much work is required to stop a 2000 kg car traveling at 20 m/s? If the friction force equals its weight, how far will it skid? W= K = - 400,000 Joules F=weight=mg=-20,000 N W=F d d=W/F=-400,000 J/-20,000N = 20.0 m

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Work Energy Work Energy W = K v = 20 m/s d=? m v = 10 m/s d= 15 m Same Friction Force

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Conservation of Energy Total Mechanical Energy, E = U +K Energy can neither be created nor destroyed only transformed from one form to another In the absence of friction or other non-conservative forces the total mechanical energy of a system does not change E f =E o

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Conservation of Energy 10.0 m m = 1.02 kg (mg = 10.0 N) K = 0 JU=100 J U = 75 J U = 50 J U = 0 J U = 25 J K = ? K = 50 J K = 25 J Constant E {E = K + U} E f = E o No friction No Air resistance

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Conservation of Energy 5.0 m m = 2.0 kg K=0 J U=100 J U = 0 J K = ? Constant E {E = K + U} Constant E {E = K + U} E f =E o No friction

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Conservation of Energy 5.0 m m = 2.0 kg K = 0 J U =100 J v = ? K = 100 J Constant E {E = K + U} Constant E {E = K + U} E f =E o No friction

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Conservation of Energy Constant E {E = K + U} E f =E o E f =E o +W other K f +U f =K o +U o +W other

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Example 8.8

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L cos(25°)

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Power Work = Power x time 1 Watt= 1 J/s 1 J = 1 Watt x 1 sec 1 kilowatt - hr = 1000 (J/s) 3600 s = 3,600,000 J Energy = $$$$$$ 1 kW-hr = $0.04 = 4 cents

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Power Work = Power x time W=P t [ J=(J/s) s= Watt * sec ] work = ? when 2000 watts of power are delivered for 4.0 sec.

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Power Energy = Power x time E =P t [ kW-hr=(kW) hr] or [ J=(J/s) s= Watt * sec ]

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Power Energy = Power x time How much energy is consumed by a 100 Watt lightbulb when left on for 24 hours? What units should we use? J,W, & s or kW-hr, kW, hr

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Power Energy = Power x time What is the power output of a duck who does 3000 J of work in 0.5 sec? What units should we use? J,W, & s or kW-hr, kW, hr

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Power Energy = Power x time E =P t [ kW-hr=(kW) hr] Energy = ? when 2000 watts (2 kW) of power are delivered for 6.0 hr. Cost at 4 cent per kW-hr?

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Machines Levers Dd f F Work in = Work out f D = F d

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Machines Levers D =8 m d = 1 m f=10 N F=? Work in = Work out f D = F d

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Machines Levers D =8 m d = 1 m f=10 N F=? Work in = Work out 10N 8m = F 1m F = 80 N

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Machines Pulleys D d f F Work in = Work out f D = F d

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Machines Pulleys D d f F Work in = Work out f D = F d D/d = 4 so F/f = 4 If F=200 N f=?

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Machines Pulleys D d f F Work in = Work out f D = F d D/d = 4 so F/f = 4 If F=200 N f = 200 N/ 4 = 50 N

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Machines Hydraulic machine D d f F Work in = Work out f D = F d if D=20 cm, d =1 cm, and F= 800 N, what is the minimum force f?

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Machines Hydraulic machine D d f F Work in = Work out f D = F d f 20 cm = 800 N (1 cm) f = 40 N if D=20 cm, d =1 cm, and F= 800 N, what is the minimum force f?

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Efficiency E in E out E loss

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Efficiency E in = 200 J E out = 150 J E loss = ?

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Machines Hydraulic machine D d f F Work in = Work out f D = F d f 20 cm = 800 N (1 cm) f = 40 N if D=20 cm, d =1 cm, and F= 800 N, what is the minimum force f?

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Machines Hydraulic machine D d f F Work in = 60 N (20 cm)=1200 N-cm Work out = 800 N (1 cm)= 800 N-cm if D=20 cm, d =1 cm, F= 800 N, and f=60 N, what is the effeciency?

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