FOR SCIENTISTS AND ENGINEERS physics a strategic approach THIRD EDITION randall d. knight © 2013 Pearson Education, Inc. Chapter 11 Lecture

© 2013 Pearson Education, Inc. Chapter 11 Work Chapter Goal: To develop a more complete understanding of energy and its conservation. Slide 11-2

© 2013 Pearson Education, Inc. The Basic Energy Model  The energy of a system is a sum of its kinetic energy K, its potential energy U, and its thermal energy E th.  The change in system energy is: 1.Energy can be transferred to or from a system by doing work W on the system. This process changes the energy of the system: -  E sys = W. 2.Energy can be transformed within the system among K, U, and E th. These processes don’t change the energy of the system: -  E sys = 0. Slide 11-22

© 2013 Pearson Education, Inc. Work and Kinetic Energy  The word “work” has a very specific meaning in physics.  Work is energy transferred to or from a body or system by the application of force.  This pitcher is increasing the ball’s kinetic energy by doing work on it. Slide 11-25

© 2013 Pearson Education, Inc. Work and Kinetic Energy  Consider a force acting on a particle which moves along the s -axis.  The force component F s causes the particle to speed up or slow down, transferring energy to or from the particle.  The force does work on the particle:  The units of work are N m, where 1 N m = 1 kg m 2 /s 2 = 1 J. Slide 11-26

© 2013 Pearson Education, Inc. The Work-Kinetic Energy Theorem  The net force is the vector sum of all the forces acting on a particle.  The net work is the sum W net =  W i, where W i is the work done by each force.  The net work done on a particle causes the particle’s kinetic energy to change. Slide 11-27

© 2013 Pearson Education, Inc. An Analogy with the Impulse-Momentum Theorem  The impulse-momentum theorem is:  The work-kinetic energy theorem is:  Impulse and work are both the area under a force graph, but it’s very important to know what the horizontal axis is! Slide 11-28

© 2013 Pearson Education, Inc. Work Done by a Constant Force  A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement.  The work done by this force is:  Here  is the angle makes relative to. Slide 11-31

© 2013 Pearson Education, Inc. Force Perpendicular to the Direction of Motion  The figure shows a particle moving in uniform circular motion.  At every point in the motion, F s, the component of the force parallel to the instantaneous displacement, is zero.  The particle’s speed, and hence its kinetic energy, doesn’t change, so W =  K = 0.  A force everywhere perpendicular to the motion does no work. Slide 11-51

© 2013 Pearson Education, Inc. The Dot Product of Two Vectors  The figure shows two vectors, and, with angle  between them.  The dot product of and is defined as:  The dot product is also called the scalar product, because the value is a scalar. Slide 11-54

© 2013 Pearson Education, Inc. Work Done by a Constant Force  A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement.  The work done by this force is: Slide 11-59

© 2013 Pearson Education, Inc. The Work Done by a Variable Force To calculate the work done on an object by a force that either changes in magnitude or direction as the object moves, we use the following: We must evaluate the integral either geometrically, by finding the area under the curve, or by actually doing the integration. Slide 11-62

© 2013 Pearson Education, Inc. Conservative Forces  The figure shows a particle that can move from A to B along either path 1 or path 2 while a force is exerted on it.  If there is a potential energy associated with the force, this is a conservative force.  The work done by as the particle moves from A to B is independent of the path followed. Slide 11-67

© 2013 Pearson Education, Inc. Nonconservative Forces  The figure is a bird’s-eye view of two particles sliding across a surface.  The friction does negative work: W fric =  k mg  s.  The work done by friction depends on  s, the distance traveled.  This is not independent of the path followed.  A force for which the work is not independent of the path is called a nonconservative force. Slide 11-68

© 2013 Pearson Education, Inc. Mechanical Energy  Consider a system of objects interacting via both conservative forces and nonconservative forces.  The change in mechanical energy of the system is equal to the work done by the nonconservative forces:  Mechanical energy isn’t always conserved.  As the space shuttle lands, mechanical energy is being transformed into thermal energy. Slide 11-69

© 2013 Pearson Education, Inc. Finding Force from Potential Energy  The figure shows an object moving through a small displacement  s while being acted on by a conservative force.  The work done over this displacement is:  Because is a conservative force, the object’s potential energy changes by  U = −W = −F s Δs over this displacement, so that: Slide 11-73

© 2013 Pearson Education, Inc. Finding Force from Potential Energy  In the limit  s  0, we find that the force at position s is:  The force on the object is the negative of the derivative of the potential energy with respect to position. Slide 11-74

© 2013 Pearson Education, Inc. Dissipative Forces As two objects slide against each other, atomic interactions at the boundary transform the kinetic energy K macro into thermal energy in both objects. Kinetic friction is a dissipative force. K  E th Slide 11-80

© 2013 Pearson Education, Inc. Dissipative Forces  The figure shows a box being pulled at a constant speed across a horizontal surface with friction.  Both the surface and the box are getting warmer as it slides.  Dissipative forces always increase the thermal energy; they never decrease it. Slide 11-81

© 2013 Pearson Education, Inc. Power  The rate at which energy is transferred or transformed is called the power P.  The SI unit of power is the watt, which is defined as: 1 watt = 1 W = 1 J/s  The English unit of power is the horsepower, hp. 1 hp = 746 W Slide Highly trained athletes have a tremendous power output.

© 2013 Pearson Education, Inc. Examples of Power Slide

© 2013 Pearson Education, Inc. Power  When energy is transferred by a force doing work, power is the rate of doing work: P = dW/dt.  If the particle moves at velocity while acted on by force, the power delivered to the particle is: Slide