Welcome back to Physics 211

1
Welcome back to Physics 211

• Todays agenda
• Internal forces
• Tension, pulleys
• Circular motion

2
Current homework assignments

• WHW6
• In blue Tutorials in Physics homework book
• HW-37 1, HW-38 2, HW-42 5, HW-45 1
• due Wednesday, Oct. 11th in recitation
• FHW3
• From end of chapters 5 6 in University Physics
• 5.55, 5.60, 5.108, 6.6
• due Friday, Oct. 13th in recitation

3
What if ? gt tan-1ms ?
F
N

• Block begins to slide
• Resolve along plane
• Wsinq?- mKWcosq? ma
• Or
• a g(sinq?- mKcosq)

W
q
4
Summary of friction

• 2 laws of friction static and kinetic
• Static friction tends to oppose motion and is
  governed by inequality
• Fs msN
• Kinetic friction is given by equality FK mKN

5
Internal Forces

• So far replaced macroscopic bodies by points
  why is this OK?
• Specifically, such body composed of (very many)
  parts neglected all internal forces of these
  parts on each other
• Also neglected rotational motion -- later

6
Simple example
A
B
A
NAG
Constant v
NAB
PAH
FAG
WAE
B
NBG
NBA
FBG
WBE
7
Composite system

• Newtons Third Law for A and B imply that we can
  consider combined system CAB in which NAB, etc.
  do not appear internal forces

NCGNAGNBG
PCH
FCFAGFBG
WCEWAEWBE
8
Internal forces summary

• Can apply Newtons laws to a composite body
• Can ignore internal forces of one part of body on
  another, since these cancel (Third law)
• Justifies treating macroscopic bodies as
  point-like

9
Tension

• For an ideal string or rope connecting two
  objects
• does not stretch ? inextensible
• has zero mass

• Lets look at an example of a cart connected to
  a falling mass by an ideal string...

10
Demo Cart attached to falling mass with string
Free body diagram for mass
Free body diagram for cart
11
What if the mass of the rope/string is not zero?
Two blocks are connected by a heavy rope. A
hand pulls block A in such a way that the blocks
move upward at increasing speed. The (downward)
tension force on the upper block by the rope is
1. less than 2. equal to 3. greater than the
(upward) tension force on the lower block by the
rope. 4. Answer depends on which block is heavier.
12
Hand pulls block A so blocks move up at
increasing speed.
13
Notice for mR 0, the tension forces exerted at
either end are the same.

• The term tension in the string is therefore
  often used as a short-hand for the tension forces
  exerted on or by the string at either end.

14
Blocks A and C are initially held in place as
shown. After the blocks are released, block A
will accelerate up and block C will accelerate
down. The magnitudes of their accelerations are
the same. Will the tension in the string be
1. equal to 1.0 N (i.e. the weight of
A), 2. between 1.0 N and 1.5 N, 3. equal to 1.5
N (i.e. the weight of C), or 4. equal to 2.5 N
(i.e. the sum of their weights)?
15
Free-body diagram for block C.
Free-body diagram for block A.
Atwoods machine
16
Demo Pulleys
2 pulleys 2T W F T W/2
T
F
N pulleys F W/N!
W
17
Forces in circular motion

• Motion around circular track, constant speed
  (for now)

arad v2/r
18
Two identical balls are connected by a string and
whirled around in circles of radius r and 2r at
constant speed. The acceleration of ball B is
1. four times as great 2. twice as great 3. equal
to 4. one half as great as the acceleration of
ball A.
19
The two balls are whirled around in a circle as
before. Assume that the balls are moving very
fast and that the two strings are massless. The
tension in string P is
1. less than 2. equal to 3. greater than the
tension in string R.
20
(No Transcript)
21
Car on circular track with friction

• Motion around circular track, constant speed
  (for now)

arad v2/r
22
Motion of car on banked circular track (no
friction)
R
car
N
a
q
W
Speed v
Horizontal forces Vertical
23
Motion on loop-the-loop
What is normal force on car at top and bottom of
loop? Neglect friction assume moves with speed
vB at bottom and vT at top
car
At bottom
At top
24
Apparent weight?

• What is criterion to just make it over loop?

25
Another example
m1
m2 falls coefficient of kinetic friction on
plane is m?
m2
q
26
Criteria for Motion?
What is largest value of m? which supports
motion? (assume q? 300, m1 1.0 kg, m2 2.0
kg)
27
Reading assignment

• Work, scalar product
• 6.1 - 6.3 in textbook