A couple of house rules Be on time Switch off mobile phones Put away laptops Being present = Participating actively
Het basisvak Toegepaste Natuurwetenschappen http://www.phys.tue.nl/nfcmr/natuur/collegenatuur.html Applied Natural Sciences Leo Pel e mail: 3nab0@tue.nl http://tiny.cc/3nab0
Chapter 6 Work and Kinetic Energy PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman The money of physics Lectures by Wayne Anderson Copyright 2012 Pearson Education Inc.
LEARNING GOALS What it means for a force to do work on a body, and how to calculate the amount of work done. The definition of the kinetic energy (energy of motion) of a body, and what it means physically. How the total work done on a body changes the body s kinetic energy, and how to use this principle to solve problems in mechanics. How to use the relationship between total work and change in kinetic energy when the forces are not constant, the body follows a curved path, or both. How to solve problems involving power (the rate of doing work). 4
Primitive Economics Do your job Get paid 5
Modern Economics Do your job Get paid Buy stuff Using money simplifies economics and accounting. 6
Why Energy Helps Motion, in general, is hard to calculate. Using forces, momentum, acceleration, etc. gets complicated because they are all vectors (have magnitude & direction). Energy is not a vector; it s just a number. Can predict motion by figuring out how much energy that motion will cost. 7
PART 2: Example of skier What is the speed of the skier downhill? (no friction) Newton: h Answer: Follows 'fast' from consideration of energy 8
Where are we Kinematics Newton s laws Classical mechanics is ready!! Why continue? 9
Where are we Kinematics Newton s laws Classical mechanics is ready!! Problem can be solved often more convenient Use laws derived from Newton s laws Laws around (conservation) energy Laws around (conservation) momentum 10
Relation Newton s laws and Energy Newton s laws Work Dutch: arbeid Energy 11
Work done by constant force The definition of work, when the force is parallel to the displacement: SI work unit: newton-meter (N m) = joule, J 12
13
Work done by force at angle If the force is at an angle to the displacement: Only the horizontal component of the force does any work (horizontal displacement). 14
Work Summary W F x SI Units for work: 1 joule = 1 J = 1 N m W F x Fcos x x 1 electron-volt = 1 ev = 1.602 x 10-19 J 16
Work done by constant force The work can also be written as the dot product of the force F and the displacement d: 17
Negative and Positive Work The work done may be positive, zero, or negative, depending on the angle between the force and the displacement: 18
Unbanked curves What is the maximum speed for friction coefficient μ? How much is work is done by friction? 1) Negative 2) 0 3) Positive 19
Perpendicular Force and Work A car is traveling on a curved highway. The force due to friction f s points toward the center of the circular path. How much work does the frictional force do on the car? Zero! General Result: A force that is everywhere perpendicular to the motion does no work. 20
Work (more general) 22
Work (more general) P2 x2 y 2 z 2 W F dl F dx F dy F dz x y z P1 x1 y1 z1 23
Example: Pulling a Suitcase A rope inclined upward at 45 o pulls a suitcase through the airport. The tension on the rope is 20 N. How much work does the tension do, if the suitcase is pulled 100 m? W T( x)cos W (20 N)(100 m)cos 45 1410 J Note that the same work could have been done by a tension of just 14.1 N by pulling in the horizontal direction. 24
Gravitational Work In lifting an object of weight mg by a height h, the person doing the lifting does an amount of work W = -mgh. If the object is subsequently allowed to fall a distance h, gravity does work W = mgh on the object. W mgh 25
Positive & Negative Gravitational Work When positive work is done on an object, its speed increases; when negative work is done, its speed decreases. 26
General definition Work done by a force on an object : W r 2 r 1 F dr dr Also useful as: force is unknown angle is not constant motion is not along straight line F result: scalar (unit J=Nm) dimension of energy 27
Work A woman holding a bowling ball still in her hand. The work she performed on the ball 1. depends on the mass of the ball. 2. can not be calculated with this information. 3. is zero. Answer: 3. There is force needed, but there is no movement, and so there is no work done. 28
Work by gravitational force A comet is approaching Earth. For the labor W A the earth during the approach to the comet is doing and the work W K done by the comet on the earth: 1. W A > 0 but W K < 0 2. W A > 0 and W K > 0 v 3. W A < 0 but W K > 0 4. W A < 0 and W K < 0 Answer: 2. For both forces are the force vector and motion vector in the same direction 29
Gravitational force is not a contact force: W A B -W B A F A K s K F s 0 s A F s 0 F K A At equal displacement(contact forces): Two objects: W A B = - W B A 30
Magnitude of the force not constant: spring 0 Force on spring: F = k x Hooke s law elastic deformations Work done by spring: By hand on spring: By spring on hand Labour can be positive or negative Two objects in contact: W A B = - W B A 31
Law work energy Due to force speed boot increases Constant force constant acceleration v v as 2 2 2 2 1 Newton: F = ma, and work hence: Definition: K = ½ m v 2, kinetic energy 2 2 v v 2 1 W Fs mas m( ) s 2s 1 1 2 2 W mv mv 2 1 2 2 Work-energy W K K K 2 1 32
Work energy more general dv ( ) dt dv dv dx dv v dt dx dt dx x2 x2 W F x dx m dx x1 x1 dv dx x2 v2 W mv dx mvdv x1 v1 1 1 W mv mv 2 2 2 2 2 1 W K K K 2 1 Work = difference in kinetic energy 33
Kinetic energy for various objects 34
Law of Work and Kinetic Energy The work done by the net force equals the change in kinetic energy W K K K 2 1 thus follows directly from Newton's laws Apply: speed / velocity change given position-dependent force force / displacement given speed / speed change 35
Problem Solving Strategy Picture: The way you choose the +y direction or the +x direction can help you to easily solve a problem that involves work and kinetic energy. Solve: 1. Draw the particle first at its initial position and second at its final position. For convenience, the object can be represented as a dot or box. Label the initial and final positions of the object. 2. Put one or more coordinate axes on the drawing. 3. Draw arrows for the initial and final velocities, and label them appropriately. 4. On the initial-position drawing of the particle, place a labeled vector for each force acting on it. 5. Calculate the total work done on the particle by the forces and equate this total to the change in the particle s kinetic energy. Check: Make sure you pay attention to negative signs during your calculations. For example, values for work done can be positive or negative, depending on the direction of the displacement relative to the direction of the force. Kinetic energy values, however, are always positive. 36
Example: A Dogsled Race During your winter break, you enter a dogsled race across a frozen lake, in which the sleds are pulled by students instead of dogs. To get started, you pull the sled (mass 80 kg) with a force of 180 N at 40 above the horizontal. The sled moves x = 5.0 m, starting from rest. Assume that there is no friction. (a) Find the work you do. (b) Find the final speed of your sled. W W F x F x total you x cos (180 N)(cos 40 )(5.0 m) 689 J W mv mv mv 1 2 1 2 1 2 total 2 f 2 i 2 f v v 2W m 2 total f f 2W 2(689 J) m (80 kg) total 4.15 m/s 37
Example: Work and Kinetic Energy in a Rocket Launch A 150,000 kg rocket is launched straight up. The rocket engine generates a thrust of 4.0 x 10 6 N. What is the rocket s speed at a height of 500 m? (Ignore air resistance and mass loss due to burned fuel.) W F y 6 9 thrust ( ) (4.0 thrust 10 N)(500 m) 2.0 10 J W w y mg y 4 2 9 grav ( ) ( ) (1.5 10 kg)(9.80 m/s )(500 m) 0.74 10 J 1 2 9 K mv 0 W 2 thrust Wgrav 1.26 10 J v 2 K m 129.6 m/s 38
Typical example of excercise The blocks in the first figure initially move at a speed v = 0.9 m/s to the right / down, but after a distance s = 2.0 m come to a halt. Calculate the coefficient of friction between block and table. Have to calculate friction force Typical Energy/Work: we know begin/end speed distance travelled 2 object: can be treated seperately 41
setup N F t y m 1 m 2 F w F t v x v m 1 g Fw kn km1 g F d r ( Fw Ft) s m 2 g F d r ( mg 2 F t ) s K 0 1 2 mv 1 2 K 0 1 2 mv 2 2 42
execute W F dr K F d r ( Fw Ft) s 1 2 K 0 mv 2 1 y F d r ( mg 2 F t ) s 1 2 K 0 m v 2 2 x 1 2 2 mv 1 ( Fw Ft) s 1 2 2 mv 2 ( mg 2 F t ) s m m v m g F s m g m g s 1 ( ) 2 ( ) ( ) 2 1 2 2 w 2 k 1 k 1 2 ( m m ) v m gs 2 1 2 2 mgs 1 F t elimineren + 0.79 F w m g k 1 43
Power Power is a measure of the rate at which work is done: James Watt (1736-1819) SI power unit: 1 J/s = 1 watt = 1 W 1 horsepower = 1 hp = 746 W 44
Power and Velocity v so v t t W F F v t W P F v t Power is the rate of energy flow. SI Units for power: 1 watt = 1 W = 1 J/s 1 hp = 550 ft lb/s = 746 W kw 6 1 kw h = (1000 W)(3600 s) = 3.6 10 W h = 3.6 MJ 3 4 45
46
Example:The Power of a Motor A small motor is used to operate a lift that raises a load of bricks weighing 500 N to a height of 10 m in 20 s at constant speed. The lift weighs 300 N. What is the power output of the motor? P F v Fv cos Fv cos 0 Fv P (500 N 300 N)(10 m/20 s) 400 W 0.54 hp 47
Summary 48
Summary 49
50