Physics 211 Lecture 7, Slide 1

1
Stuff you asked about
5x pudding
Talk more about work.
go over boxes being pulled on a table by a string
connected to a box hanging off the table
How much of the calculus do we need to know?
Why did you change from fading in each equation
and circling the important bits to just throwing
all the integrations and whatnot onto one
eye-bending page?
all of them, especially the ball on the curved
slope problem
I'm incredibly unfamiliar with vector calculus,
and I'd like you to clarify how to combine
vectors with integrals properly. Seriously. It's
making me rethink how I've been doing physics in
high school and kind of scaring me.
The physics of massive amounts of bunnies in a
very small box that is moving across a pile of
frictionless bunnies with a constant
acceleration. I don't know if there is an
equation for that...
Please put this on the lecture slides in class
tomorrow. It's my dream to be on it.
2
Physics 211 Lecture 7
Today's Concepts Work Kinetic Energy
3
The Dot Product
4
Work Kinetic Energy Theorem
The work done by force F as it acts on an object
that moves between positions r1 and r2 is equal
to the change in the objects kinetic energy
5
If the force is constant and the directions
arent changing then this is very simple to
evaluate
F
d
Car
In this case
since cos(0)1
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A lighter car and a heavier truck, each initially
at rest, are pushed with the same constant force
F. After both vehicles travel a distance d, which
of the following statements is true? (Ignore
friction)
Act
Car
Truck

• A) The will have the same velocity
• B) They will have the same kinetic energy
• C) They will have the same momentum

7
Derivation not so important
Concept very important
A force pushing over some distancewill change
the kinetic energy
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Work done by gravity near the Earths surface
path
mg
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Work done by gravity near the Earths surface
dlN
dl1
dl2
mg
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Work done by gravity near the Earths surface
dlN
dl1
dl2
mg
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Work Kinetic Energy Theorem
If there are several forces acting then W is the
work done by the net (total) force
12
Preflight

• Three objects having the same mass begin at the
  same height, and all move down the same vertical
  distance H. One falls straight down, one slides
  down a frictionless inclined plane, and one
  swings on the end of a string.
• In which case does the object have the biggest
  net work done on it by all forces during its
  motion?

H
Free Fall Frictionless incline
String
A) Free Fall B) Incline C) String D)
All the same
13
Act

• Three objects having the same mass begin at the
  same height, and all move down the same vertical
  distance H. One falls straight down, one slides
  down a frictionless inclined plane, and one
  swings on the end of a string.
• What is the relationship between their velocities
  when they reach the bottom?

H
Free Fall Frictionless incline
String
A) Vf gt Vi gt Vp B) Vf gt Vp gt Vi
C) Vf Vp Vi
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Preflight/Act
H
Free Fall Frictionless incline
String
A) Vf gt Vi gt Vp B) Vf gt Vp gt Vi
C) Vf Vp Vi
Only gravity will do work Wg mgH 1/2 mv22 -
1/2 mv12 1/2 mv22
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A car drives up a hill with constant speed. Which
statement best describes the total work WTOT done
on the car by all forces as it moves up the hill?
Preflight/Act
v

• WTOT 0
• WTOT gt 0
• WTOT lt 0

A) velocity is not changing, and therefore the
work (which equals change in kinetic energy) is
zero.
B) The net force and the distance are in the same
direction.
C) The car is moving against gravity so work is
negative.
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From Monday
A box sits on the horizontal bed of a moving
truck. Static friction between the box and the
truck keeps the box from sliding around as the
truck drives.
?S
a
If the truck moves with constant accelerating to
the left as shown, which of the following
diagrams best describes the static frictional
force acting on the box
A
B
C
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Preflight/Act
A box sits on the horizontal bed of a moving
truck which his accelerating to the left as
shown. Static friction between the box and the
truck keeps the box from sliding.
F
?S
a
D
The work done on the box by the static frictional
force as the truck moves a distance D is A)
Positive B) Negative C) Zero
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Work done by a spring
x1
0
FS
19
Act
A box sliding on a horizontal frictionless
surface runs into a fixed spring, compressing it
a distance x1 from its relaxed position while
momentarily coming to rest. If the initial speed
of the box were doubled and its mass were halved,
how far x2 would the spring compress ?
A) B)
C)
x1
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Act Solution
v
x1
If v is doubled and m is halved
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Work done by gravity in general
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Act
In Case 1 we send an object from the surface of
the earth to a height above the earth surface
equal to one earth radius. In Case 2 we start
the same object a height of one earth radius
above the surface of the earth and we send it
infinitely far away. In which case is the
magnitude of the work done by the Earths gravity
on the object biggest?
A) Case 1 B) Case 2 C) They are
the same
Case 2
Case 1
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Act Solution
Case 1
Case 2
RE
Case 1
2RE