Physics 2211: Lecture 16 Todays Agenda

1
Physics 2211 Lecture 16Todays Agenda

• Work Energy
• Work done by multiple constant forces
• Work done by weight

2
Review Constant Force
Work, W, of a constant force F acting through
a displacement ?r is W F? ?r F ?r cos(?)
Fr ?r
F
?r
?
Fr
displacement
3
Work/Kinetic Energy Theorem

• Net Work done on object
• change in kinetic energy of object
• WF ?K 1/2mv22 - 1/2mv12

WF F?x
m
4
What about multiple forces?
Suppose FNET F1 F2 and the displacement is
?r. The work done by each force is W1 F1? ?r
W2 F2 ? ?r WTOT W1 W2
F1? ?r F2? ?r (F1 F2 )? ?r
WTOT FTOT? ?r Its the total force
that matters!!
FNET
F1
?r
F2
5
A simple applicationWork done by gravity on a
falling object

• What is the speed of an object after falling a
  distance H, assuming it starts at rest?
• Wg F? ?r mg ?r cos(0) mgH
• Wg mgH
• Work/Kinetic Energy Theorem
• Wg mgH 1/2mv2

v0 0
mg
j
?r
H
v
6
Work done by gravity

• Wg F? ?r mg ?r cos ?
• -mg ?y
• Wg -mg ?y
• Depends only on ?y !

m
mg
?r
?
-?y
m
7
Work done by gravity...
W NET W1 W2 . . . Wn

• Depends only on ?y,
• not on path taken!

m
mg
?y
j
8

• Three objects of mass m begin at height h with
  velocity 0. One falls straight down, one slides
  down a frictionless inclined plane, and one
  swings on the end of a pendulum. What is the
  relationship between their velocities when they
  have fallen to height 0?

(a) Vf gt Vi gt Vp (b) Vf gt Vp gt Vi
(c) Vf Vp Vi
9
Only gravity will do work Wg mgH 1/2 mv22 -
1/2 mv12 1/2 mv22
does not depend on path !!
10
Lifting a book with your handWhat is the total
work done on the book??

• First calculate the work done by gravity
• Wg mg? ?r -mg ?r
• Now find the work done bythe hand
• WHAND FHAND? ?r FHAND ?r

FHAND
?r
v const a 0
mg
11
Example Lifting a book...

• Wg -mg ?r
• WHAND FHAND ?r
• WNET WHAND Wg
• FHAND ?r - mg ?r
• (FHAND - mg) ?r
• 0 since ?K 0 (v const)
• So WTOT 0!!

FHAND
?r
v const a 0
mg
12
Example Lifting a book...

• Work/Kinetic Energy Theorem says W ?K
• Net Work done on object change in kinetic
  energy of object
• In this case, v is constant so ?K 0and so W
  must be 0, as we found.

FHAND
?r
v const a 0
mg
13
Work done by Variable Force (1D)

• When the force was constant, we wrote W F ?x
• area under F vs. x plot
• For variable force, we find the areaby
  integrating
• dW F(x) dx.

F
Wg
x
?x
14
Work/Kinetic Energy Theorem for a Variable Force
dv
F
dx
F
dx
dv
dv
dv
v
(chain rule)
dx


dx
dt
dx
dt
dv
dx
v
dx
v dv
v22
v12
v22
v12
15
Recap of todays lecture

• Review
• Work done by gravity near the Earths surface
• Examples
• pendulum, inclined plane, free fall
• Work done by variable force