Week 7, Chapter VIIWeek 7, Chapter VIIKinetic Energy and WorkKinetic Energy and WorkWorkWork--Kinetic Energy TheoremKinetic Energy TheoremWork Done by a Gravitational ForceWork Done by a Gravitational ForceWork Done by a Spring ForceWork Done by a Spring ForceWork Done by a General Variable ForceWork Done by a General Variable ForceEnergy and WorkEnergy and WorkKinetic energyKinetic energyWork done by a constant forceWork done by a constant forceWorkWork--kinetic energy theoremkinetic energy theoremSample Problem VIISample Problem VII--22Two industrial spies sliding an initially stationary 225 kg flooTwo industrial spies sliding an initially stationary 225 kg floor safe a r safe a displacement displacement ddof magnitude 8.50 m, straight toward their truck. The of magnitude 8.50 m, straight toward their truck. The push push FF11of spy 001 is 12.0 N, directed at an angle of 30of spy 001 is 12.0 N, directed at an angle of 30ººdownward downward from the horizontal; the pull from the horizontal; the pull FF22of spy 002 is 10.0 N, directed at 40of spy 002 is 10.0 N, directed at 40ººabove the horizontal. The magnitudes and directions of these forabove the horizontal. The magnitudes and directions of these forces ces do not change as the safe moves, and the floor and safe make do not change as the safe moves, and the floor and safe make frictionless contact.frictionless contact.a)a)What is the net work done on the safe by the What is the net work done on the safe by the forces forces FF11and and FF22during the displacement during the displacement dd??b)b)During the displacement, what is the work WDuring the displacement, what is the work Wggdone on the safe by the gravitational force done on the safe by the gravitational force FFggand what is the work done on the safe by the and what is the work done on the safe by the normal force normal force NNfrom the floor?from the floor?c)c)The safe is initially stationary. What is its The safe is initially stationary. What is its speed vspeed vffat the end of the 8.50 m at the end of the 8.50 m displacement?displacement?Work Done by a Gravitational ForceWork Done by a Gravitational ForceWork done by gravitational forceWork done by gravitational forceChange in kinetic energyChange in kinetic energyTomato thrown upwardTomato thrown upwardLifting/lowering an objectLifting/lowering an objectSample Problem VIISample Problem VII--66An elevator cab of mass m = 500 kg is descending with An elevator cab of mass m = 500 kg is descending with speed vspeed vii= 4.0 m/s when its supporting cable begins to = 4.0 m/s when its supporting cable begins to slip, allowing it to fall with constant acceleration slip, allowing it to fall with constant acceleration aa= = gg/5./5.a)a)During the 12 m fall, what is the work WDuring the 12 m fall, what is the work WTTdone done by the upward pull by the upward pull TTof the elevator cab?of the elevator cab?b)b)What is the net work W done on the cab during What is the net work W done on the cab during the fall?the fall?c)c)During the fall through a distance d = 12 m, what During the fall through a distance d = 12 m, what is the work Wis the work Wggdone on the cab by the done on the cab by the gravitational force Fgravitational force Fgg??d)d)What is the cab’s kinetic energy at the end of the What is the cab’s kinetic energy at the end of the 12 m fall ?12 m fall ?Work Done by a Spring ForceWork Done by a Spring ForceHooke’s Hooke’s lawlawWork done by a spring forceWork done by a spring forceSample Problem VIISample Problem VII--88A cumin canister of mass m = 0.40 kg slides across a A cumin canister of mass m = 0.40 kg slides across a horizontal frictionless counter with a speed of horizontal frictionless counter with a speed of v = 0.50 m/s. It the runs into and compresses a spring of v = 0.50 m/s. It the runs into and compresses a spring of spring constant k = 750 N/m. When the canister is spring constant k = 750 N/m. When the canister is momentarily stopped by the spring, by what distance d is momentarily stopped by the spring, by what distance d is the spring compressed?the spring compressed?Work Done by a General Work Done by a General Variable ForceVariable ForceWork: variable forceWork: variable forceCalculusCalculusDivide area under curveDivide area under curveAdd increments of W (numerically)Add increments of W (numerically)Analytical form?Analytical