Phys101 Lectures 7 Work And Kinetic Energy - SFU.ca

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Phys101 Lectures 7Work and Kinetic EnergyKey points: Work Done by a Force Scalar Product of Two Vectors (dot product) Kinetic Energy and the Work-Energy PrincipleRef: 6-1,2,3.Page 1

Work Done by a Constant ForceThe work done by a constant force is defined asthe distance moved multiplied by the componentof the force in the direction of displacement:yW Fx xx

Scalar Product of Two VectorsDefinition of the scalar product (dot product):Component form : A B Ax Bx Ay By Az BzThe work done by a force is the dot productbetween the force and the displacement

i-clicker question 7-1Is it possible to do work on anA) yesobject that remains at rest?B) no

Example: Work done on a crate.A person pulls a 50-kg crate 40 m along a horizontal floor by a constantforce FP 100 N, which acts at a 37 angle as shown. The floor issmooth and exerts no friction force. Determine (a) the work done byeach force acting on the crate, and (b) the net work done on the crate. WP FP x FP x cos ( 100 )( 40 ) cos 37 3200 ( J ) WN FN x FN x cos 90 0 WW mg x mgx cos 90 0the net work done on the crate:WNET WP 3200 J

i-clicker question 7-2:A box is beingFriction and WorkA) friction does no work at allpulled across aB) friction does negative workrough floor at aC) friction does positive workconstant speed.What can yousay about thework done byfriction?W 0 when 90 Force and displacement are inopposite directions.

i-clicker question 7-3: Does the Earth do workon the Moon?The Moon revolvesaround the Earth in anearly circular orbit, withapproximately constanttangential speed, keptthere by the gravitationalforce exerted by theEarth. Does gravity do(A) positive work,(B) negative work, or(C) no work at all on theMoon?

Work Done by a Varying ForceFor a force that varies, the work can beapproximated by dividing the distance up intosmall pieces, finding the work done duringeach, and adding them up.W Fx x area under the F-x curve.

Work Done by a Varying ForceWork done by a spring force:xThe force exerted by aspring is given byHooke’s law:Meaning of negative sign:It’s a restoring force,always pointing to theequilibrium position.The magnitude of FS is proportionalto the displacement from theequilibrium position.

Work Done by a Varying ForcePlot of F vs. x.When the spring is stretched byx, The work done by the appliedforce is equal to the shaded area.1WP ( height base )211 2 kx x kx22FSxx1 2WS kx2FSx kxWork done by the spring is:11 2WS kx x kx22

Example: Work done on a spring.(a) A person pulls on a spring, stretching it 3.0 cm, which requiresa maximum force of 75 N. How much work does the person do?(b) If, instead, the person compresses the spring 3.0 cm, howmuch work does the person do?(a) Can we do this: W (75N)(0.030m) 2.25J ?i-clicker question 7-4: (A) Yes; (B) No.Why? Or Why not?1 2WP kx2But how do we find k ?FP FS ( kx ) kx,FP75k 2500 N / mx 0.031 2 1WP kx ( 2500 )( 0.03 )2 1.1 ( J )22(b) The same as (a) because the sign of x doesn’t change the value of x2.Physically, compressing a spring is equally hard as stretching.

The Work-Energy PrincipleThe net work done on an object is equal to theincrease in kinetic energy of the object:It's a consequence of Newton's 2nd law :For example, for 1 - d motion with constant accelerati on Wnet F d ma d ma( x2 x1 ) (for 1 - d motion, 0)1 m( v22 v12 )2 sincev 2 v02 2a( x x0 ) x

The Work-Energy PrincipleIt allows us to solve certain problems withoutknowing the details of motion and forcesbetween the initial and final states.On the other hand, Newton’s law is aninstantaneous relationship between the net forceand acceleration. It requires detailed informationabout the net force throughout the course ofmotion.

Example: Work to stop a car.A car traveling 60 km/h can brake to a stop within a distance d of 20 m.If the car is going twice as fast, 120 km/h, what is its stoppingdistance? Assume the maximum braking force is approximatelyindependent of speed.x 1 2 1 21 2Wnet F d Fd mv2 mv1 mv1222m 2i .e., d v1 v122F when v1 is doubled, d should be quadrupled : 4 20m 80m.

each force acting on the crate, and (b) the net work done on the crate. W P F P x F P xcosT ( 100)( 40 ) cos37q 3200 ( J ) & & W N F N x F N xcos90 q 0 & & W W mg x mgxcos90 q 0 & & the net work done on the crate: W NET W P 3200 J. i-clicker question 7-2: Friction and Work

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