Transcript Ch33

Chapter 7. Newton’s Third Law
Chapter Goal: To use
Newton’s third law to
understand interacting
objects.
Ch. 7 – Student Learning Objectives
• To learn how two objects interact.
• To identify action/reaction pairs of forces.
• To understand and use Newton’s third law.
• To understand how to use propulsion forces and
tension forces.
OMIT section 7.2 (#1-7) in workbook, but
don’t xxxxx it out
• We’ll do a modification during class.
Newton’s Third Law
Action-reaction Pair
If object A exerts a force on object B, then object B
exerts a force on object A. The pair of forces (due to one
interaction), is called an action/reaction pair.
The action/reaction pair will never appear in the same
free body diagram.
Tactics: Analyzing interacting objects
Example - analyzing interacting objects
A person pushes a large crate
across a rough surface.
• Identify the objects that are
systems of interest
• Draw free-body diagrams for
each system of interest.
• Identify all action/reaction
pairs with a dashed line.
Forces involved in pushing a crate – FBD of
person and crate
Propulsion Force
• The force label fp
shows that the
static friction force
on the person is
acting as a
propulsion force.
• This is a force that
a system with an
internal source of
energy uses to
drive itself forward.
Propulsion forces
Freebody Diagrams – Workbook exercises 1-7
Draw a freebody diagram of each object in the
interacting system.
Show action/reaction pair with red/orange dotted lines.
Draw force vectors in another color.
Label vectors with standard symbols.
Label action/reaction pairs FAonB , FBonA for example.
A fishing line of negligible mass lifts a fish
upward at constant speed. The line and the fish
are the system, the fishing pole is part of the
environment. What, if anything, is wrong with
the free-body diagrams?
A fishing line of negligible mass lifts a fish
upward at constant speed. The line and the fish
are the system, the fishing pole is part of the
environment. What, if anything, is wrong with
the free-body diagrams?
The gravitational force and the tension
force are incorrectly identified as an
action/reaction pair. The correct
action reaction pair is…?
Action/reaction pairs are never on the
same free body diagram.
Mass of line considered negligible so no
weight force necessary.
Acceleration constraint
• An acceleration
constraint is a welldefined relationship
between the acceleration
of 2 (or more) objects.
• In the case shown, we
can assume ac =aT = ax
Is there an acceleration constraint in this
situation? If so, what is it? The pulley is
considered to be massless and frictionless.
Answer: Acceleration constraint is: aA = -aB
The actual signs may not be known until the problem
is solved, but the relationship is known from the start.
Workbook exercises 12-16 + “17”
17
answers
a2kg = -.5a1kg
Boxes A and B are sliding to the right across a
frictionless table. The hand H is slowing them
down. The mass of A is larger than the mass of B.
Rank in order, from largest to smallest, the
horizontal forces on A, B, and H. Ignore forces on
H from objects not shown in the picture.
Boxes A and B are sliding to the right across a
frictionless table. The hand H is slowing them
down. The mass of A is larger than the mass of B.
Rank in order, from largest to smallest, the
horizontal forces on A, B, and H.
FB on H = FH on B > FA on B = FB on A
from Newton’s 2nd and 3rd Laws
Problem-Solving Strategy: InteractingObjects Problems
EOC #8
Two strong magnets each weigh 2 N and are on
opposite sides of the table. The table, by
itself, has a weight of 20 N. The long rangerange attractive force between the magnets
keeps the lower magnet in place. The
magnetic force on the lower magnet is 3 times
its weight.
a. Draw a fbd for each magnet and table. Use
dashed lines to connect all action/reaction
pairs.
b. Find the magnitude of all forces in your fbd
and list them in a table.
EOC #8
Upper
Table
Lower
FBDs for EOC 8
EOC #8 - Answer
Ranking Task – Pushing blocks
Block 1 has a mass of m,
block 2 has a mass of 2m,
block 3 has a mass of 3m.
The surface is frictionless.
Rank these blocks on the basis
of the net force on each of
them, from greatest to least.
If the net force on each
block is the same, state that
explicitly
Ranking Task – Pushing blocks
Answer: 3
2
1
Reason: ΣF = ma.
Acceleration is equal for all
blocks.
EOC #10
Block 1 has a mass of 1 kg, block 2
has a mass of 2 kg, block 3 has a
mass of 3 kg. The surface is
frictionless.
a. Draw a fbd for each block. Use
dashed lines to connect all action/
reaction pairs.
b. How much force does the 2-kg
block exert on the 3-kg block?
c. How much force does the 2-kg
block exert on the 1-kg block?
EOC #10- Answer
b. How much force does the 2-kg block exert on the 3-kg block? – 6N
c. How much force does the 2-kg block exert on the 1-kg block? – 10N
Page 163, 2nd Ed (Found in Chapter 5, 1st ed)
Interacting systems problem (EOC #35)
A rope attached to a 20 kg
wooden sled pulls the sled
up a 200 snow-covered hill.
A 10 kg wooden box rides
on top of the sled. If the
tension in the rope steadily
increases, at what value of
tension will the box slip?
Interacting systems problem (EOC #35)
What are the objects of
interest?
What kind of axes for the FBD
for each?
Acceleration constraints?
Draw FBDs, with 3rd law pairs
connected with dashed lines.
Find the max tension in the
rope, so the box does not
slip.
Box: 3 forces
Sled: 6 forces
0.06
0.06
• I suggest starting with the
equations for the sled, since
the unknown of interest is
found there.
• Identify quantities in sled
equations that you can find
by solving box equations.
• Solve box equations.
• Return to sled equations
with newfound booty.
• Plug and chug.
Interacting systems problem (EOC #35)
A rope attached to a 20 kg
wooden sled pulls the sled
up a 200 snow-covered hill.
A 10 kg wooden box rides
on top of the sled. If the
tension in the rope steadily
increases, at what value of
tension will the box slip?
Answer: 155 N.
The Massless String Approximation
A horizontal forces only fbd for the string:
TAonS
●
TBonS
ΣF = TBonS – TAonS = ma. If string is accelerating to the right
TBonS = TAonS + ma
The Massless String Approximation
Often in physics and engineering problems the mass of the
string or rope is much less than the masses of the objects
that it connects. In such cases, we can adopt the following
massless string approximation:
This allows the objects A and B to be analyzed as if
they exert forces directly on each other.
Pulleys
If we assume that the string is massless and the
pulley is both massless and frictionless, no net force
is needed to turn the pulley. TAonB and TBonA act “as
if” they are an action/reaction pair, even though
they are not acting in opposite directions.
Pulleys
• In this case the Newton’s 3rd
law action/reaction pair
point in the same direction!
T 100kg on m
Tm on 100kg
All three 50 kg blocks are at rest. Is the
tension in rope 2 greater than, less than,
or equal to the tension in rope 1?
A. Equal to
B. Greater than
C. Less than
All three 50 kg blocks are at rest. Is the
tension in rope 2 greater than, less than,
or equal to the tension in rope 1?
A. Equal to
B. Greater than
C. Less than
In the (moving)
figure to the right,
is the tension in
the string greater
than, less than, or
equal to the
weight of
block B?
A. Equal to
B. Greater than
C. Less than
In the figure to the
right, is the
tension in the
string greater
than, less than, or
equal to the
weight of
block B?
A. Equal to
B. Greater than
C. Less than
Interacting systems problem (EOC #40)
A 4.0 kg box (m) is on a
frictionless 350 incline. It
is connected via a massless
string over a massless,
frictionless pulley to a
hanging 2.0 kg mass (M).
When the box is released:
a. Which way will it go
George?
b. What is the tension in the
string?
4.0 kg
350
Interacting systems problem (EOC #40)
a. Which way will it go?
Even if you have no clue,
follow the plan!
What are the objects of
interest?
What kind of axes for the
FBD for each?
Acceleration constraints??
Draw FBDs, with 3rd law
pairs connected with dashed
lines.
4.0 kg
350
Interacting systems problem (EOC #40)
How do you figure out
which way the system
will move, once m is
released from rest?
massless string
approx. allows us to
join the tensions as an
“as if” interaction pair
Interacting systems problem (EOC #40)
Interacting systems problem (EOC #40)
a = - 0.48 m/s2, T = 21 N.
Which way is the system moving?
How does the tension compare to the
tension in the string while the box
was being held?
Greater than, less than, equal to?
EOC # 33
The coefficient of static friction is
0.60 between the two blocks in the
figure. The coefficient of kinetic
friction between the lower block
and the floor is 0.20. Force F
causes both blocks to slide 5
meters, starting from rest.
Determine the minimum amount of
time in which the motion can be
completed without the upper block
slipping.
EOC # 33
The coefficient of static
friction is 0.60
between the two blocks
in the figure. The
coefficient of kinetic
friction between the
lower block and the
floor is 0.20. Force F
causes both blocks to
slide 5 meters, starting
from rest. Determine
the minimum amount
of time in which the
motion can be
completed without the
upper block slipping.
EOC # 33
amax = 3.27 m/s2
tmin = 1.75 s (time is important
in this one)
EOC # 46
Find an expression for F, the
magnitude of the horizontal
force for which m1 does not
slide up or down the wedge.
This expression should be in
terms of m1, m2 , θ, and any
known constants, such as g.
All surfaces are frictionless.
EOC # 46
.
EOC # 46
.
F = (m1 + m2) g tan θ
EXAMPLE 7.6 Comparing two tensions
QUESTION:
EXAMPLE 7.6 Comparing two tensions
EXAMPLE 7.6 Comparing two tensions
EXAMPLE 7.6 Comparing two tensions
EXAMPLE 7.6 Comparing two tensions
A small car is pushing
a larger truck that
has a dead battery.
The mass of the truck
is larger than the
mass of the
car. Which of the following statements is true?
A. The truck exerts a larger force on the car than the car exerts
on the truck.
B. The truck exerts a force on the car but the car doesn’t exert a
force on the truck.
C. The car exerts a force on the truck but the truck doesn’t exert
a force on the car.
D. The car exerts a larger force on the truck than the truck
exerts on the car.
E. The car exerts the same amount of force on the truck as the
truck exerts on the car.
A small car is pushing
a larger truck that
has a dead battery.
The mass of the truck
is larger than the
mass of the
car. Which of the following statements is true?
A. The truck exerts a larger force on the car than the car exerts
on the truck.
B. The truck exerts a force on the car but the car doesn’t exert a
force on the truck.
C. The car exerts a force on the truck but the truck doesn’t exert
a force on the car.
D. The car exerts a larger force on the truck than the truck
exerts on the car.
E. The car exerts the same amount of force on the truck as
the truck exerts on the car.