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Kinetic Energy and Work; Potential Energy;Conservation of Energy. Lecture 07 Thursday: 5 February 2004 Slide 2 Slide 3 Slide 4 Slide 5 Slide 6 WORK Work provides a means of determining the motion of an object when the force applied to it is known as a function of position. For example, the force exerted by a spring varies with position: F=-kx where k is the spring constant and x is the displacement from equilibrium. Slide 7 WORK (Constant Force) Slide 8 WORK (Variable Force) Slide 9 Work Energy Theorem W net is the work done by F net the net force acting on a body. Slide 10 Work Energy Theorem (continued) Slide 11 Slide 12 Work Energy Theorem (concluded) Define Kinetic Energy Then, W net = K f - K i W net = K Slide 13 Slide 14 Slide 15 Slide 16 Slide 17 Recall Our Discussion of the Concept of Work Work has no direction associated with it (it is a scalar). However, work can still be positive or negative. Work done by a force is positive if the force has a component (or is totally) in the direction of the displacement. Slide 18 CONSERVATIVE FORCES A force is conservative if the work it does on a particle that moves through a closed path is zero. Otherwise, the force is nonconservative. Conservative forces include: gravitational force and restoring force of spring. Nonconservative forces include: friction, pushes and pulls by a person. FgFg d Slide 19 CONSERVATIVE FORCES If a force is conservative, then the work it does on a particle that moves between two points is the same for all paths connecting those points. This is handy to know because it means that we can indirectly calculate the work done along a complicated path by calculating the work done along a simple (for example, linear) path. Slide 20 Work Done by Conservative Forces is of Special Interest The work done in the course of a motion, is undone in if you move back. This encourages us to define another kind of energy (as opposed to kinetic energy) - a stored energy associated with conservative forces. We call this new type of energy potential energy and define it as follows: U = W c FgFg d Slide 21 Potential Energy Associated with the Gravitational Force Slide 22 Potential Energy Associated with the Spring Force We know (or should know) from our homework, Slide 23 Tying Together What We Know about Work and Energy U = W c W net = K So, under the condition that there are only conservative forces present : W net = W c In that case, K = U K + U = 0 Slide 24 The Bottom Line E i = E f K i + U i = K f + U f The Total Mechanical Energy of a System is the sum of Kinetic and Potential energies. This is what is conserved or constant. u Gravitational force: U= mgh u Restoring force of a spring: U =1/2kx 2 u (KE=1/2mv 2 ) Slide 25 An Example A 70 kg skate boarder is moving at 8 m/s on flat stretch of road. If the skate boarder now encounters a hill which makes an angle of 10 o with the horizontal, how much further up the road will the he be able to go without additional pushing? Ignore Friction. Slide 26 10 o h d KE i +U i =KE f +U f (only conservative forces) so KE i + 0 = 0+U f (U i =0 and KE f =0) 1/2mv 2 = mgh 1/2v 2 = gh h = v 2 /(2g) = 8 2 /(2*9.8) = 3.26 m h/d = Sin 10 o d = 18.8 m