
Today’s lecture will cover Textbook Sections 6.5 - 6.8
Physics 101: Lecture 10, Pg 1

• Work: Transfer of Energy by Force
• W
F
= | F | | S | cos

•Kinetic Energy (Energy of Motion)
•K = 1/2 mv 2
• Work-Kinetic Energy Theorem:
• S
W =
D
K
• Potential (Stored) Energy U

Physics 101: Lecture 10, Pg 2 07

What concepts were most difficult to understand in preparing for this lecture?
“The difference between conservative and nonconservative forces”
“I’ve been mainly focused on the Exam tomorrow so to be
Honest I haven’t been following this pre-lecture all too closely…”
“Nothing”
“It’s all a little confusing… :/” Math / symbols / subscripts
“The idea of Work is harder to understand.”
Physics 101: Lecture 10, Pg 3


Example 1: Drop ball
W g
= (mg)(S)cos 
S = h
W g
= mghcos(0 0 ) = mgh
D y = y f
-y i
= -h
W g
= -mg D y
Y i i
Physics 101: Lecture 10, Pg 4 10

 Example 2: Toss ball up
W g
= (mg)(S)cos 
S = h
W g
= mghcos(180 0 ) = -mgh
D y = y f
-y i
= +h
W g
= -mg D y mg
S
Y f
= h
Y i
= 0 y x
Physics 101: Lecture 10, Pg 5 13

 Example 3: Slide block down incline
W g
= (mg)(S)cos 
S = h/cos 
W g
= mg(h/cos  )cos 
W g
= mgh
D y = y f
-y i
= -h
W g
= -mg D y h mg

S
Physics 101: Lecture 10, Pg 6 16

“I didn't understand what U was”
 Work done by gravity independent of path
 W g
= -mg (y f
- y i
)
 Define U g
=mgy
 Works for any CONSERVATIVE force
 Modify Work-Energy theorem

W nc
 D
K
 D
U
Physics 101: Lecture 10, Pg 7 20

“The idea of non-conservative forces - not quite sure what this means”
Which of the following statements correctly define a
Conservative Force:
A.
A force is conservative when the work it does on a moving object is independent of the path of the motion between the object's initial and final positions.
B. A force is conservative when it does no net work on an object moving around a closed path, starting and finishing at the same point.
C. Both of the above statements are correct. correct
D. Neither of the above statements is correct.
Physics 101: Lecture 10, Pg 8 23

A skier goes down a 78 meter high hill with a variety of slopes.
What is the maximum speed she can obtain if she starts from rest at the top?
Conservation of energy:
S
W nc
=
D
K +
D
U
0 = K f
-K i
+ U f
- U i
K i
+ U i
= K f
+ U f
½ m v i
2 + m g y i
= ½ m v f
2 + m g y f
0 + g y i
= ½ v f
2 + g y f v f
2 = 2 g (y i
-y f
) v f
= sqrt( 2 g (y i
-y f
)) v f
= sqrt( 2 x 9.8 x 78) = 39 m/s
Physics 101: Lecture 10, Pg 9 26

 As the pendulum falls, the work done by the string is
1) Positive 2) Zero 3) Negative
W = F d cos  . But  = 90 degrees so Work is zero.
How fast is the ball moving at the bottom of the path?
Conservation of Energy (W nc
=0)
S
W nc
=
D
K +
D
U
0 = K final
- K initial
+ U final
- U initial
K initial
+ U initial
= K final
0 + mgh = ½ m v 2 final
+U
+ 0 final v final
= sqrt(2 g h) h
Physics 101: Lecture 10, Pg 10 30

With no regard for his own personal safety your physics professor will risk being smashed by a bowling ball pendulum! If released from a height h, how far will the bowling ball reach when it returns?
Conservation of Energy (W nc
=0)
S
W nc
=
D
K +
D
U
0 = K final
- K initial
+ U final
- U initial
K initial
+ U initial
= K final
+U final
0 + mgh initial
= 0 + mgh final h initial
= h final h
Physics 101: Lecture 10, Pg 11

Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball get to the bottom first?
A. Dropping correct
B. Slide on ramp (no friction)
C. Swinging down
D. All the same
1 2 3
49%
“The ball that is simply dropped has the quickest path to the ground, which is a straight line.”
0%
1%
1%
10% 20% 30% 40%
49%
“They all start at rest and travel the same distance, so they all reach the bottom at the same time with the same speed.”
50%
Physics 101: Lecture 10, Pg 12 31

Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed?
0%
1. Dropping
2. Slide on ramp (no friction)
3. Swinging down
4. All the same correct
1
8%
16%
20%
20% 40%
56%
60%
2 3
Conservation of Energy (W nc
=0)
S
W nc
=
D
K +
D
U
K initial
+ U initial
= K final
+U final
0 + mgh = ½ m v 2 final
+ 0 v final
= sqrt(2 g h)
Physics 101: Lecture 10, Pg 13 35

A 50 kg skier goes down a 78 meter high hill with a variety of slopes. She finally stops at the bottom of the hill. If friction is the force responsible for her stopping, how much work does it do?
Work Energy Theorem:
W nc
= K f
-K i
+ U f
U i
= ½ m v f
2 - ½ m v i
2 + m g y f
– m g y i
= 0+0+0 - g y i m
= – 764 x 50 Joules
= -38200 Joules
Similar to bob sled homework
Physics 101: Lecture 10, Pg 15 40

How high will the pendulum swing on the other side now?
A) h
1
> h
2 h
1 m
B) h
1
= h
2 h
2
C) h
1
< h
2
Conservation of Energy (W nc
=0)
S
W nc
=
D
K +
D
U
K initial
+ U initial
= K final
+U final
0 + mgh
1 h
1
= 0 + mgh
2
= h
2
Physics 101: Lecture 10, Pg 16 44

 P = W /
D t
 Units: Joules/Second = Watt

How much power does it take for a
(70 kg) student to run up the stairs in
141 (5 meters) in 7 seconds?
P = W / t
= m g h / t
= (70 kg) (9.8 m/s 2 ) (5 m) / 7 s
= 490 J/s or 490 Watts
Physics 101: Lecture 10, Pg 17 48


Conservative Forces
» Work is independent of path
» Define Potential Energy U
 U gravity
= m g y
 U spring
= ½ k x 2

Work – Energy Theorem

W nc
 D
K
 D
U

Chapter 6, problems 27, 31, 35

Good Luck on EXAM!
Physics 101: Lecture 10, Pg 18 50