Physics 121C Mechanics Lecture 12 Newtons 3rd Law October 29, 2004

1
Physics 121C - MechanicsLecture 12Newtons
3rd LawOctober 29, 2004

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

2
Announcements

• Homework Assignment 4 is now posted and is due
  on Tycho by 900 PM on Wednesday, November 3
  (i.e., next week).
• The solutions for Exam 1 (done using Mathematica)
  are posted on the Web. Click on the Exam 1
  link on the Course Schedule.
• The Physics 121C web site had to be reconfigured
  because I was exceeding my disk-space limit on my
  UW faculty account with lecture files. One
  reliable way to get to the course web is to go to
  my main account at http//faculty.washington.edu/j
  cramer and click on Teaching. This should take
  you to the Physics 121C Syllabus, this contains
  all the links to other pages of interest for
  Physics 121C.

3
Exam 1 Statistics
Average 57.5 Std Dev 15.1
High 92 Median 56 Low 24
1.7
2.7
3.7
4
Lecture Schedule (Part 2)
You are here!
5
Newtons 3rd Law

• Newtons 3rd Law Every force occurs as one
  member of an action/reaction pair of forces.
• The two members of the action/reaction force pair
  act on two different objects.
• The two members of the action/reaction pair are
  equal in magnitude and opposite in direction

Alternate Wording For every action there is an
equal and opposite reaction.
Implication of Newtons Laws the interaction is
the principal item of interest the force is an
aspect of the interaction.
Consequence of Newtons 3rd Law a closed
isolated system cannot accelerate due to internal
motions (the no space-drive theorem).
6
Identifying Action/Reaction Pairs

• Draw each object separately. Place them in the
  correct position relative to other objects. Dont
  forget to include objects like the earth that may
  not be mentioned in the problem.
• Identify every force. Draw the force vector on
  the object on which it acts. Label each with a
  subscripted label such as . The usual
  force symbols, such as and can be used.
• Identify the action/reaction pairs. Force
  goes with force . Connect the two
  force vectors of each action/reaction pair with a
  dotted line. When youre done, there should be no
  unpaired forces.
• Identify the objects that are systems of
  interest. Other objects whose motion you dont
  care about are part of the environment.
• Draw a free-body diagram for each system of
  interest. Include only the forces acting on the
  system, not forces that the system exerts on
  other objects.

7
3rd Law Reasoning
8
Example Accelerating Boxes
The hand pushes box A, which pushes box B
across a frictionless table. The mass of B is
greater than the mass of A. Rank the
horizontal forces.
9
Acceleration Constraints
The car and truck have the same acceleration,
i.e., aCaT.
The string constrains the two blocks to
accelerate together, so aA aB.
Strategy Examine the connections between
objects (strings, ropes, ) and determine how
these connections constrain and couple the motion
of the objects. Use those constraints in writing
equations of motion.
10
Interacting-System Strategy

• MODEL Identify which objects are systems and
  which are part of the environment. Make
  simplifying assumptions.
• VISUALIZEPictorial representation. Show
  important points in the motion with a sketch. You
  may want to give each system a separate
  coordinate system. Define symbols and identify
  what the problem is trying to find. Include
  acceleration constraints as part of the pictorial
  model. Physical representation. Identify all
  forces acting on each system and all
  action/reaction pairs. Draw a separate free-body
  diagram for each system. Connect the force
  vectors of action/reaction pairs with dotted
  lines. Use subscript labels to distinguish
  forces, such as and that act
  independently on more than one system.
• SOLVE Use Newtons second and third laws
• Write the equations of Newtons second law for
  each system, using the force information from the
  free-body diagrams.
• Equate the magnitudes of action/reaction pairs.
• Include the acceleration constraints, the
  friction model, and other quantitative
  information relevant to the problem.
• Solve for the acceleration, then use kinematics
  to find velocities and positions.
• ASSESS Check that your result has the correct
  units, is reasonable, and answers the question.

11
Example Keep the Cratefrom Sliding (1)
A 200 kg crate of priceless works of art is
loaded on the back of a 2,000 kg truck. As you
press down on the accelerator, FT propels the
truck forward. How big can FT be without the
crate sliding? Assume ms0.8, mk0.3 and mr0.
Constraint aCx aTx ax
3rd Law Pairs nT on C Û nC on T and fT on C Û
fC on T
12
Example Keep the Cratefrom Sliding (2)
13
Clicker Question 1
a. FB on H FH on B FA on B FB on A
b. FB on H FH on B gt FA on B FB on A
c. FB on H FH on B lt FA on B FB on A
d. FH on B FH on A gt FA on B
14
Tension Revisited
Tension forces within the rope are due to
stretching the spring-like molecular bonds.

• If the safe is in equilibrium (at rest or moving
  with a constant speed), then Fnet0.Thus, TR on
  S wE on S.
• If the safe is accelerating, then FnetmSagt0.
  Thus, TR on S ¹ wE on S.

15
Example Pulling a Rope (1)
1
2
A student pulls horizontally with a force of 100
N on a rope that is attached to a wall.
Two students pulls on opposite ends of a rope
with forces of 100 N each.
Clicker Question 2Which tension is larger?
a. T1gtT2 b. T1T2 c. T1ltT2
16
Example Pulling a Rope (2)
3rd Law TL on RTR on L
2nd Law TR on L FS1 on L 100 N 2nd Law TL
on R FS2 on L 100 N
2nd Law TR on LFS on L100 N
3rd Law TL on R TR on L 100 N
Question What does the wall do to the rope?
17
Clicker Question 3
a. T1gtT2 b. T1T2 c. T1ltT2
18
The Massless String Approximation
Isolate the string and consider the forces
on it (Fnet)x TA on STB on S mSa,so TA on
S TB on S mSa ¹TB on S
A horizontal acts on a block that is
connected to another block by a string.
Consider the constraints and forces.
Massless String ApproximationAssume that mS0
so that TA on S TB on S
19
Example Comparing Tensions
Blocks A and B are connected by massless
string 2 and pulled across a frictionless surface
by massless string 1. The mass of B is larger
than the mass of A. Is the tension in string
2 smaller, equal, or larger than the tension in
string 1?
The blocks must be accelerating to the
right, because there is a net force in that
direction. We use the massless string
approximation to directly relate the string
tensions on A and B due to string 2 TA on
BTB on A (FA net)xT1-TB on A
T1-T2 mAaAx so T1 T2
mAaAx Therefore, T1 gt T2.
20
Pulleys
Massless String Approximation
Strings and ropes often pass over pulleys
that change the direction of the tension. In
principle, the friction and inertia in the pulley
could modify the transmitted tension.
Therefore, it is conventional to assume that such
pulleys are massless and frictionless.
Massless and Frictionless Pulley Approximation
21
Example Mountain Climbing (1)
A 90 kg mountain climber is suspended from
ropes as shown. Rope 3 can sustain a maximum
tension of 1500 N before breaking. What is
the smallest that angle q can become before the
rope breaks?
22
Example Mountain Climbing (2)
23
Example Stagecraft (1)
A 200 kg set used in a play is stored in a
loft above the stage. The rope holding the set
passes up and over a pulley, then is tied
backstage. The director tells a 100 kg stagehand
to lower the set. He unties the set, holds on to
the rope, and is hoisted into the loft. What
is his acceleration? (Assume a massless
rope and a massless frictionless pulley.)
24
Example Stagecraft (2)
25
Example A Bank Robbery (1)
Bank robbers have pushed a 1,000 kg safe to
a second-story floor-to-ceiling window. The plan
to break the window and lower the safe 3.0 m to
their truck. They stack up 500 kg of furniture,
tie a rope between the safe and the furniture,
place the rope over a pulley, and push the safe
out the window. What is the safes speed
when it hits the truck bed? (Assume mk0.5
between the furniture and the floor.)
26
Example A Bank Robbery (2)
27
Clicker Question 4
A small car is pushing a larger truck that
has a dead battery. The mass of the truck is
much larger than the mass of the car. Which of
the following statements is true?
a. The car exerts a force on the truck, but the
truck doesnt exert a force on the car.
b. The car exerts a larger force on the truck
than the truck exerts on the car.
c. The car exerts the same force on the truck as
the truck exerts on the car.
d. The truck exerts a larger force on the car
than the car exerts on the truck.
e. The truck exerts a force on the car, but the
car doesnt exert a force on the truck.
28
Chapter 8 Summary (1)
29
Chapter 8 Summary (2)
30
Review of Newtons Laws
31
End of Lecture 12

• Before the next lecture, read Knight,Chapters
  9.1 through 9.3.
• Homework Assignment 4 should be submitted on
  the Tycho system by 900 PM, on Wednesday, Nov.
  3.(24 hours late Þ 70 credit)
• If you have not already done so, registeryour
  clicker athttp//faculty.washington.edu/jcramer/
  ph121c/Clicker