-Conservative and

Non-Conservative Forces

-Changes in Mechanical Energy in the Presence

of FrictionAP Physics CMrs. Coyle

What happens when friction is present?

• When friction is present, the work done by the frictional force W=fd is transferred to heat energy.

• The sum of the potential and kinetic energy of the system is not conserved.

• Friction is a “non-conservative” force.

A Force is “Non-Conservative” if:

• “the work it does on an object that moves between two points depends on the path taken.”

• “the work it does on an object that moves through a round trip is not zero.”

• Example: friction, tension, normal force, propulsion forces.

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.

In the presence of friction, the mechanical energy of the system will decrease.

• The change in mechanical energy will be negative and will equal the work done by friction.

• ΔEmech =Emech final -Emech initial =-fd

Example 1 (#)21 A 4 kg particle moves from the origin to

position C, having coordinates x=5m and y=5m. One force on the particle is the gravitational force acting in the negative y direction. Using W= F·r = Frcosθ, calculate the work done in going from O to C along a)OAC, b) OBC, c) OC.

(See Fig. 1 on next slide.) Your results should be all identical. Why?

(Ans: -196J)

Fig.1

B C(5m,5m)

O A

Example 2 (#31)The coefficient of friction between the3kg block and the surface is 0.4. The system starts from rest. What is the speed of the 5kg ball when it has fallen 1.5m?

Ans: 3.74m/s

Example 3(#38)

• A 75.0kg skysurfer is falling straight down with a terminal speed of 60m/s. Determine the rate at which the skysurfer-Earth system is losing mechanical energy.

(Ans: dE mech =mgv= 44.1kW)

dt