Work, Energy and Power Ms Houts AP Physics C Chapters 7 & 8 2008 by W.H. Freeman and Company Definition of Work The work done by a constant force F applied to an object that moves through a displacement x is defined as Work is a scalar quantity that can be positive or negative. Forces applied in the direction of motion is positive. Forces applied opposite the direction of motion 2008 by W.H. Freeman and Company fkfk Definition of Kinetic Energy An object moving with velocity v and mass m has a kinetic energy given by: 2008 by W.H. Freeman and Company Work-Kinetic Energy Theorem The total work done on a particle is equal to the change in its kinetic energy. Work-Kinetic Energy Example 1 A 6-kg box is raised from rest a distance of 3 meter by a vertical force of 80 N. Find the work done by the force, the work done by gravity, and the final speed of the box. Graphical Interpretation of Work Work is the area under the Force-position graph. Work with a variable force The work done by a force F that varies with position x is given by This integral equals the area under the F- versus-x curve. Work-Kinetic Energy Example 2 A spring that obeys Hookes Law rests on a frictionless surface. Hookes Law gives the force of a spring as F=-kx Find the work done by the spring force when it is stretched from x = 0 to x = x f. Practice Exercises with Work Further practice- pages Work in three dimensions Only the component of the force in the direction of the displacement does work. If a force and displacement have components then the work done by the force is given by Dot Product The dot product is the product of two vectors A and B, where we consider only the part of A that lies in the direction of B, or the part of B that lies in the direction of A. Work as the Dot Product The work done by a constant force F over a displacement s is If the force varies with position, then the work is given by Properties of Scalar Products Power Power is the rate at which work is done. Since or in derivative form Power in 3 dimensions Practice problems, p. 162 Conservative Forces A force is conservative if the total work it does on a particle is zero when the particle moves along any closed path returning to its initial position. Potential Energy Functions Doing work against a conservative force stores energy. When the conservative force does work on a particle, that energy is released. 2008 by W.H. Freeman and Company Gravitation Potential Energy The work done by the gravitational force in lifting up a weight a distance y is negative, since the force is opposite the displacement. The change in gravitational potential energy is positive. Spring Potential Energy Using the Potential Energy to Find the Force Since the potential energy is the negative of the integral of the force function: Then the negative of the derivative of the potential energy function is the force function. Equilbrium A particle is in equilibrium if the net force acting on it is zero. Since the force is the derivative of the potential energy function, the equilibrium points can be found graphically from a potential energy graph by finding places where the slope of the graph is zero. 2008 by W.H. Freeman and Company In stable equilibrium, a small displacement results in a restoring force That accelerates the particle back toward its equilibrium position. 2008 by W.H. Freeman and Company In unstable equilibrium, a small displacement results in a force that accelerates the particle away from its equilibrium position. 2008 by W.H. Freeman and Company In neutral equilibrium, a small displacement results in zero force and the particle remains in equilibrium.