Announcements
• Test 1 next Thursday, 5–7 PM
• Covers material in Chapters 2–5
• Review session
– Monday 5:30–7 PM, CR 103
– Bring your questions
Group Work
1. Rank the following scenarios from least
work done to most work done.
A.
100 N
10 m
100 N
D.
B.
100 m
10 N
100 m
100 N
C.
E.
100 N
100 m
0m
Work
force is not all that matters
§ 6.1–6.2
What’s the point?
Energy is critically important to Nature.
Objectives
• Relate work to force and distance.
• Calculate the kinetic energy of a moving
object.
CPS Question
Work is
A. Force  time.
B. Force  distance
C. Force / distance.
D. Force / time.
E. Mass  velocity
Work
Formula
W = work = F·s
F = force applied
s = displacement
Units of Work
joule (J) = 1 newton along 1 meter
kg m
kg m2
J = Nm =
m
=
s2
s2
Group Work
2. Estimate the work done by the
strong man in the video. Show your
work! Justify your estimates of force
and distance.
Work is a Scalar
component of
force in direction
of motion
Source: Griffith, The Physics of Everyday Phenomena
Dot Product of Vectors
a
f
a·b = ab cos f
a
b
b
Commutative
Dot Product Geometrically
• Product of the projection of one vector onto the
other
• “Overlap”
a
ab cos f
f
b
Dot Product by Components
If
A = Axi + Ayj + Azk
B = Bxi + Byj + Bzk
then
A·B = AxBx + AyBy + AzBz
Dot Product Properties
• Positive if |f| < p/2
• Negative if |f| > p/2
–
+
• Zero if vectors perpendicular (|f| = p/2)
• Maximum magnitude if parallel or antiparallel
CPS Question
The piglet has a choice of three frictionless
slides to descend. Along which slide is the
greatest net force exerted on the piglet?
A
B
C
D. The net force is the same for all.
CPS Question
The piglet has a choice of three frictionless
slides to descend. Along which slide would
the piglet slide the longest distance?
A
B
C
D. The distance is the same for all.
CPS Question
The piglet has a choice of three frictionless
slides to descend. Along which slide would
the piglet finish soonest?
A
B
C
D. The time is the same for all.
Group CPS Question
The piglet has a choice of three frictionless
slides to descend. Along which slide would
gravity do the most work on the piglet?
A
D. Same work for all.
B
C
E. Need more information.
Group Work
• Problem 4 on the worksheet
– use sum of products of components
Total (Net) Work
If several forces act on a moving object:
s
F4
F1
F2
• W = (SF)·s
or
• W = S(F·s)
F3
Example Problem 6.57
A luggage handler at the Laramie Airport pulls a
20-kg suitcase up a ramp inclined at 25° above the
horizontal with a force of 140 N parallel to the
ramp. The coefficient of kinetic friction between
the ramp and the box is mk = 0.30. the suitcase
travels 3.80 m along the ramp. Find
a. the work done on the suitcase by the handler
b. the work done on the suitcase by gravity
c. the work done on the suitcase by the normal force
d. the work done on the suitcase by friction
e. the total work done on the suitcase
f. the final speed of the suitcase, if its initial speed was zero
CPS Question
To accelerate an object from 10 to 20 m/s
requires
A. more work than to accelerate from 0 to
10 m/s.
B. the same amount of work as to
accelerate from 0 to 10 m/s.
C. less work than to accelerate from 0 to 10
m/s.
Work of Acceleration
• To accelerate to speed v with constant force F
slope = a =
v
F
=
m
t
v
area = Dd
speed
time
• Work = F·Dd
t
mv
1
Dd = 2 vt
F = m (slope) = t
mv
1
1
2
mv
vt
=
• Work = 2
2
t
Another Perspective
• So, for the 0–10 vs. 10–20 m/s case:
• If same force, then same time
– a’s and Dv’s are equal, so Dt’s are equal
• Average speeds are 5 vs. 15 m/s
• The 10–20 m/s case travels 3 as far
A Moving Object Can Do Work
Source: Griffith, The Physics of Everyday Phenomena
Kinetic Energy
the work to bring a motionless object to
speed
KE =
1
2
mv2
equivalent to
the work a moving object does in stopping
CPS Question
Which has more kinetic energy?
A.
10 kg
10 m/s
5 kg
10 m/s
5 kg
40 m/s
10 kg
20 m/s
B.
C.
D.
CPS Question
The piglet has a choice of three frictionless
slides to descend. Along which slide would
the piglet finish with the highest speed?
A
B
C
D. The final speed is the same for all.
Work-Energy Theorem
• If an amount of work w is done on an
otherwise isolated system, the system’s
energy changes by an amount DE = w.