1. Nonconservative Forces

2. When conservative forces act on a system ΔK + ΔU = 0 Most moving objects experience nonconservative forces – forces that remove energy from the system - friction - drag force In this case the ΔK + ΔU ≠ 0. It equals the work done by the nonconservative force ΔK + ΔU = W nc Our Energy formula becomes E i = E f + W nc **Even through the work done is negative we add it to the final energy side of the equation. It is in the form of heat lost to the system

3. Example : One of the tallest and fastest roller coasters in the world is the Steel Dragon in Mie, Japan. The ride includes a vertical drop of 93.5 m. The coaster has a speed of 3.0 m/s at the top of the drop. The speed at the bottom is 41.0 m/s. Find the work done by the nonconservative forces on a 55.0 kg rider during the descent.

4. Example: A 60 kg sledder starts from rest and slides down a 20 o incline 100 m long. (a) If the coefficient of friction is 0.090, what is the sledder’s speed at the base of the incline. (b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the sledder travel along the level snow? U

5. © 2013 Pearson Education, Inc. Power  The rate at which energy is transferred or transformed is called the power P.  The SI unit of power is the watt, which is defined as: 1 watt = 1 W = 1 J/s Slide 11-98 Highly trained athletes have a tremendous power output. If the particle moves at velocity while acted on by force, the power delivered to the particle is:

6. © 2013 Pearson Education, Inc. Example 11.13 Choosing a Motor Slide 11-99 58,800 W

7. © 2013 Pearson Education, Inc. Four students run up the stairs in the time shown. Which student has the largest power output? QuickCheck 11.11 Slide 11-103

8. © 2013 Pearson Education, Inc. Four students run up the stairs in the time shown. Which student has the largest power output? QuickCheck 11.11 Slide 11-104

9. © 2013 Pearson Education, Inc. Example 11.14 Power Output of a Motor Slide 11-105 882 W