Lecture 13 Potential Energy difference The difference between the points A and B associated with the conservative force F is the negative of the work done by the conservative force in moving the body along any path connection the points A and B Potential energy difference Constant gravity Force Work Potential Energy Worked Example Change in Potential Energy for Inverse Square Gravitational Force Consider an object of mass m moving towards the sun mass m Initially the object is at a distance r from the center of the sun The object moves to a nal distance r from the center of the sun For the object sun system what is the change in potential energy during this motion Potential Energy difference Spring force Force Work done Potential energy change Zero Point Potential Energy Work Energy Theorem Conservative Forces When the only forces acting on the object are conservative forces then the change in potential energy is Energy Principle Meaning there is no non conservative work 0 E is the same as saying E is constant Energy Diagrams Identify system Identify state of system before interaction and state of nal states Draw energy diagrams for these states including Example Block Sliding off Hemisphere A small point like object of mass m rests on top of a sphere of radius R The object is released from the top of the sphere with a negligible speed and it slowly starts to slide and g is the magnitude of the gravitational acceleration The block loses contact with the surface of the sphere at an angle 1 with respect to the vertical What is the speed of the object at the instant it loses contact with the surface of the sphere 1 Choice of zero point P for potential energy for each interaction in which potential energy difference is well de ned 2 Draw speed of all objects in system 3 Identify initial and nal mechanical energy E K U
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