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

AP Physics CMrs. 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.”

• “the work this force does on an object that moves through a round trip is zero.”

• Example: gravity, force of a spring.

### Consider a ball thrown up and the system is the ball and the earth.

• The work done by the force of gravity Wg =-ΔU

### 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

• Find F

• Find F(x):

### 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.

xmax and –xmax :

turning points

### 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

### 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).