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-Relating Conservative Force and Potential Energy -Energy diagrams and Equilibrium

-Relating Conservative Force and Potential Energy -Energy diagrams and Equilibrium. AP Physics C Mrs. Coyle. A Force is “Conservative” if:. “ the work this force does on an object that moves between two points depends only on the position of these two points and not on the path.”

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-Relating Conservative Force and Potential Energy -Energy diagrams and Equilibrium

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  1. -Relating Conservative Force and Potential Energy-Energy diagrams and Equilibrium AP Physics CMrs. Coyle

  2. A Force is “Conservative” if: • “ the work this force does on an object that moves between two points depends only on the position of these two points and not on the path.” • “the work this force does on an object that moves through a round trip is zero.” • Example: gravity, force of a spring.

  3. Consider a ball thrown up and the system is the ball and the earth. • The work done by the force of gravity Wg =-ΔU

  4. For a particle moving along the x-axis (one dimensional motion)while a conservative force, in the same axis, within the system acts on it: ΔU is the change in potential energy of the system

  5. Solving for Fx:

  6. Example: Find the gravitational force for a particle a distance x above the earth’s surface. • Start with U= mgx • Find F

  7. Example: Find the spring force for a particle attached to a spring: • Start with U= ½ kx2 • Find F(x):

  8. Types of Positions of Equilibrium • Stable Equilibrium: movement away from this (x=0) position results in a restoring force. • Unstable Equilibrium: movement away from this position results in a force directed away from x=0 • Neutral equilibrium: movement away from x=0 does not result in either restoring nor disruptive forces.

  9. Energy Diagrams, U(x) vs x

  10. -Energy Diagrams -U(x) is minimum at x=0 (stable equilibrium) xmax and –xmax : turning points

  11. Unstable equilibriumU(x) is max

  12. Neutral EquilibriumU(x) is constant

  13. Example 1 (#40) A single conservative force acting on a particle varies as F=(-Ax+Bx2 )i N, where A and B are constants and x is in meters. a) Calculate the potential energy function taking U=0 at x=0 b) Find the change in potential energy and change in kinetic energy as the particle moves from x=2.00m to x=3.00m

  14. Example 2 (#42) • A potential energy function for a two dimensional force is U=3x3y - 7x • Find the force that acts at the point (x, y) • Hint find F(x) and F(y).

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