Phys101 Lectures 7 Work And Kinetic Energy - SFU.ca
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
Phys101 Lecture 2 - 3 Position, Displacement and Distance Position: x (when t 0, x 0; when t 50 s, x 40 m) Displacement:Δx x 2–x 1 40–0 40m (change in position) Δx represents how far the object is from its starting point, regardless of how it got there (blue line). Distance (d
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A ball of mass m 2.60 kg, starting from rest, falls a vertical distance h 55.0 cm before striking a vertical coiled spring, which it compresses an amount Y 15.0 cm. Determine the spring stiffness constant of the spring. Assume the spring has negligible mass, and ignore air resistance. Measure all distances from the point where the ball first
The instantaneous angular velocity: Angular Quantities. . at rest, and the center moves with velocity . In (b) the same wheel is seen from a reference frame where C is at rest. Now point P is . The net external
For a top player, a tennis ball may leave the racket on the serve with a speed of 55 m/s (about 120 mi/h). If the ball has a mass of 0.060 kg and is in contact with the racket for about 4 ms (4 x 10-3 s), estimate the average force on the ball. [Solution] 800( ) 0.004 0.06 55 0 N t mv t p F
the tension F T in the supporting cable. F First, FBD of the beam. Then, 0 0 0 T T F mg Mg F sin F F F cos Hy T Hx T & g N sin M m F F l F l sin Mgl mg T T T 794 2 2 solve for : 0 2 0 T W F Hx F T cosT T 687 N N F Hy mg Mg F T sin 123 T
There will be a total of four Peerwise exercises, corresponding to the four parts of the course (lectures 1-10 and exam 1, lectures 11-20 and exam 2, lectures 21-29 and exam 3, lectures 30-37 and the final exam). Log into the Peerwise "Biochemistry 508_spring 2018" by clicking on the
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