8-1 Conservative and Nonconservative ForcesDefinition 1: The total work around a closed path is

zero for a conservative force.

Work done by gravity = -mgh Work done by gravity = +mgh

Total work around a closed path = -mgh + mgh = 0. The force of gravity is a conservative force.

Ch 8 Potential Energy and Conservation of Energy

Conservative Force Definition 2: The work is independent of the path for a conservative force.

W1 + W2 = 0W1 + W3 = 0W2 = W3 = -W1

WA

WB

Path 1

WTotal

WA

WB

Path 2

WTotal

P8.3a (p.233)

F

F

x

x

AA

BB

Concept Question 1: P8.3 If the mass increases, the work done by the spring will

A. increase.

B. decrease.

C. stay the same.

8-2 Potential Energy and the Work Done by Conservative Forces

A. Potential Energy WC = -U

WC = the work of the conservative force

B. Gravity U = mgy with U = 0 at y = 0 near

the Earth’s surface

P8.57 (p.237)

C. Springs (ideal) U = kx2/2 with U = 0 at x = 0.

P8.9 (p.234)

Concept Question 2:P8.57 The change in Ug from 90 to 45 degrees is

A. greater than that from 45 to 0 degrees.

B. less than that from 45 to 0 degrees.

C. the same as that from 45 to 0 degrees.

8-3 Conservation of Mechanical Energy Mechanical Energy E = U + K W = K (Ch. 7) For a conservative force WC = -U

-U = K U + K = 0 = E E is constant or conserved P8.17 (p.234)

Concept Question: Consider a system where the force is all conservative. The initial kinetic energy is 4 J, the final kinetic energy is 8 J and the final potential energy is 5 J. What was the initial potential energy?

A. 8 J

B. 9 J

C. 9 N

D. 8 N

E. 5 J

Concept Question 5:P8.17 If the mass doubles, the change in height of the ball

A. double.

B. halve.

C. stay the same.

P8.22 (p.235)Similar to P8.18

K, U, E vs. Compression

00.10.20.30.40.50.60.7

0 0.02 0.04 0.06

Compression (m)

En

erg

y (J

)

K

U

E

8-4 Work Done by Nonconservative Forces

WTOT = WC + WNC = K (Ch. 7)

-U + WNC = K

WNC = K + U

WNC = E

P8.86 (p.239)

Concept Question 4:P8.86 If the mass is multiplied by 4, the speed will

A. quadruple (4x)

B. double.

C. stay the same.

D. halve.

E. quarter (1/4).

A Ball Rolling on a Frictionless Track

8-5 Potential Energy Curves and Equipotentials

Gravitational Potential Energy Versus Position for the Track Shown in the Previous Slide

A Mass on a Spring

U = kx2/2

Conceptual Questions: An object starts from point A. CT6: The speed at A is the same as at B,C,D,E,F,G?CT7: The speed is the greatest at B,C,D,E,F,G?

A Contour Map – an example of an equipotential plot

All the numbered lines are at the same gravitational potential energy.

P8.46 (p.236)

8.6J

4.7m0.3m

P8.81 (p.238)

P8.83 (p.239)