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**Unformatted text preview: **1 Chapter 6: Conservation of Energy Work by a Constant Force Kinetic Energy Potential Energy Work by a Variable Force Springs and Hookes Law Conservation of Energy Power 2 6.1 The Law of Conservation of Energy The total energy of the Universe is unchanged by any physical process. The three kinds of energy are: kinetic energy, potential energy, and rest energy. Energy may be converted from one form to another or transferred between bodies. 3 4 Energy forms in this chapter Kinetic energy (translational motion) gravitational energy Elastic potential energy 5 Work Work is an energy transfer that occurs when a force acts on an object that moves. If there is no displacement, no work is done and no energy is transferred. Mg = 220 N h = 4.0 m W = 220 N X 4.0 m = 880 N.m 6 6.2 Work by a Constant Force Work is an energy transfer by the application of a force. For work to be done there must be a nonzero displacement. The unit of work and energy is the joule (J). 1 J = 1 Nm = 1 kg m 2 /s 2 . 7 It is only the component of the force in the direction of the displacement that does work. An FBD for the box at left: x y F w N The work done by the force F is: ( 29 x F r F W x x F = = cos r x F r x 8 The work done by the force N is: = N W The normal force is perpendicular to the displacement. The work done by gravity ( w ) is: = g W The force of gravity is perpendicular to the displacement. 9 The net work done on the box is: ( 29 ( 29 x F x F W W W W g N F net = + + = + + = cos cos 10 In general, the work done by a force F is defined as cos r F W = where F is the magnitude of the force, r is the magnitude of the objects displacement, and is the angle between F and r (drawn tail-to-tail). Work is a Scalar can be positive , negative , or zero depending on the angle. 11 Example: A ball is tossed straight up. What is the work done by the force of gravity on the ball as it rises? FBD for rising ball: x y w r y mg y w W g - = = 180 cos 12 Example: A box of mass m is towed up a frictionless incline at constant speed. The applied force F is parallel to the incline. What is the net work done on the box? F w N F x y cos sin =- = =- = w N F w F F y x Apply Newtons 2 nd Law: 13 The magnitude of F is: sin mg F = If the box travels along the ramp a distance of x the work by the force F is sin cos x mg x F W F = = The work by gravity is ( 29 sin 90 cos x mg x w W g - = + = Example continued: 14 Example continued: The work by the normal force is: 90 cos = = x N W N The net work done on the box is: sin sin net = + - = + + = x mg x mg W W W W N g F 15 Example: What is the net work done on the box in the previous example if the box is not pulled at constant speed?...

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