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Chapter 8 Potential Energy and Conservation of Energy

Chapter 8 Potential Energy and Conservation of Energy. 8-6 Conservation of Energy 8-1 Work and Potential Energy 8-2 Path Independence of Conservative Forces 8-3 Determining Potential Energy Values 8-4 Conservation of Mechanical Energy 8-5 Work Done on a System by an External Force and

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Chapter 8 Potential Energy and Conservation of Energy

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  1. Chapter 8 Potential Energy and Conservation of Energy 8-6 Conservation of Energy 8-1 Work and Potential Energy 8-2 Path Independence of Conservative Forces 8-3 Determining Potential Energy Values 8-4 Conservation of Mechanical Energy 8-5 Work Done on a System by an External Force and Thermal Energy due to Friction

  2. 8-6 Conservation of Energy Energy of a System Conservation of Energy Principle For a system of objects Work Kinetic Energy Theorem For a Single Object: Change in Kinetic energy Change in Energy Work done by an (external) force on the object/system Change in Kinetic energy Change in Potential energy Change in thermal energy Change in internal energy However we will not worry about DEint in phys101, and we’ll deal only with situation where DEint =0

  3. 8-6 Conservation of Energy Energy of a System A particle-earth system A spring-block system Fext Fg Fs Fext Fs is not an external force Fg is not an external force If we choose our system to be a particle or a block only, then Fg and Fs will be an external force to our system (which is a single body now)

  4. 8-2 Work and Potential Energy Gravitational Potential Energy A particle-earth system Fg Fg initial final If Fext = 0 for this system then W = 0, but we know that DK is not zero as the ball falls.. So where is the energy coming from to increase its kinetic energy? We associate what is called a Potential Energy Ug with the configuration of the earth particle system, the change of which is the negative of the work done by gravitational force: DUg = -Wg

  5. 8-3 Path Independence of Conservative Forces Conservative Forces Work done by a conservative force does not depend on the path between the initial and final point. W1 W1=W2 W2 In another words: The net work done by a conservative force on a particle moving around any closed path is zero. W=0

  6. 8-3 Path Independence of Conservative Forces Non-Conservative Forces Non-Conservative Force Work depends on the path Example:

  7. 8-3 Determining Potential Energy Values Definition of Potential Energy It is defined for a system of two or more objects It is defined only for conservative forces Gravitational Potential Energy, Ug Elastic Potential Energy, Us

  8. 8-3 Determining Potential Energy Values Checkpoint Checkpoint: A particle moves from x =0 to x=1, under the influence of a conservative force as shown. Rank according to DU, most positive first (descending order).

  9. 8-3 Determining Potential Energy Values Example • What is the U of the sloth-earth system if our reference point is • at the ground • at a balcony floor that is 3.0 m above the ground • at the limb • 1 meter above the limb?

  10. 8-4 Conservation of Mechanical Energy Mechanical Energy Emech = K+U Mechanical energy Potential energy Kinetic energy If there is no external acting on a system (W = 0) and its thermal energy is constant (no non-conservative forces such as friction, DEth = 0), then its mechanical energy is conserved. Mechanical Energy is conserved 0 = DK+DU OR Kf+Uf= Ki+Ui=constant

  11. 8-4 Conservation of Mechanical Energy Checkpoint Rank according to speed at point B. Ball sliding on a Frictionless Ramp

  12. 8-4 Work Done on a System No friction involved We have a block-floor-earth system. The applied force F is external to the our system. The law of conservation of energy states that the work done by external force on a system is equal to the change of energy W = DE same height 0 Fd= DK+DU

  13. 8-4 Work Done on a System friction involved We have a block-floor-earth system, this time there is friction. The friction force is now an internal force. However as a result of the friction force, there will be a loss in the kinetic energy which appear as an increase in the thermal energy (converted to heat) of the system. It can be shown that the change in thermal energy is equal to the negative of the work done by the friction force: DEth= fk d = - Wf W = DE W = DEmech+DEth 0 Therefore the conservation of energy principle can also be stated in the form: W + Wf = DEmech F d= DK+DU+DEth fk d

  14. 8-4 Work Done on a System Example By what distance d is the spring compressed when the block stops? OR W = DEmech+DEth W + Wf = DEmech DEth = - Wf = fk d

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