Transcript F - ILM.COM.PK

Newtons’s Laws
Chapters 4&5
Chapter 4:
Forces and Newton’s Laws of Motion
Section 1:
Concepts of Force and Mass
Introducing Forces
 A force is a push or pull on an object.
 Forces are what cause an object to accelerate, or to
change its velocity by speeding up, slowing down, or
changing direction.
 It is important that we learn to identify all the forces
acting on an object, and to draw these forces as
vectors.
 Contact forces arise from physical contact.
Drawing Forces
 What are the forces acting on a book as it rests on
the table?
Table pushes up
on the book
FT
Textbook
Gravity pulls down
on the book
FG
Two Methods of Drawing Forces
 Force Diagram
 Free Body Diagram
FT
FT
Textbook
FG
FG
Sample problem:
 Draw a force diagram and a free body diagram for a
monkey hanging motionless by two arm from two
vines attached to neighboring trees.
Mass
 Mass is a measure of the amount of “stuff”
contained in an object.
 It is the measure of how much inertia an object
has.
 Scalar value
 Measured in kg
Chapter 4:
Forces and Newton’s Laws of Motion
Section 2:
Newton’s First Law of Motion
1st Law Of Motion - Inertia
 An object remains in constant motion unless acted
upon by and unbalanced force
 It is often said that the Law of Inertia violates
“common sense”. Why do you think some people
say that?
 If there is zero net force on a body, it cannot
accelerate, and therefore must move at constant
velocity. This means:
the body cannot turn.
F

0

the body cannot speed up.
The body cannot slow down.
Mass and Inertia
 Chemists like to define mass as the amount of “stuff”
or “matter” a substance has.
 Physicists define mass as inertia, which is the ability
of a body to resist acceleration by a net force.
 What is the relationship between mass and inertia?
 Inertia is the natural tendency of an object to remain
at rest in motion at a constant speed along a straight
line.
 The mass of an object is a quantitative measure of
inertia.
 Measured in kilograms (kg)
Net Force
 The net force on an object is the vector sum of all
forces acting on that object.
 The SI unit of force is the Newton (N).
Individual Forces
4N
10 N
Net Force
6N
Net Forces
Individual Forces
Net Force
5N
3N
64
4N
Question #1
When you sit on a chair, the resultant force on you is
A) zero.
B) up.
C) down.
D) depends on your weight.
E) depends on the angle of the chair
Question #2
If an object is moving can you conclude there are forces acting
on it? If an object is at rest, can you conclude there are no
forces acting on it? Consider each of the following situations.
In which one of the following cases, if any, are there no forces
acting on the object?
a) A bolt that came loose from a satellite orbits the earth at a
constant speed.
b) After a gust of wind has blown through a tree, an apple falls
to the ground.
c) A man rests by leaning against a tall building in downtown
Dallas.
d) Sometime after her parachute opened, the sky diver fell
toward the ground at a constant velocity.
e) All of the above
Question #3
A child is driving a bumper car at an amusement park. During one interval
of the ride, she is traveling at the car’s maximum speed when she
crashes into a bumper attached to one of the side walls. During the
collision, her glasses fly forward from her face. Which of the following
statements best describes why the glasses flew from her face?
a) The glasses continued moving forward because there was too little force
acting on them to hold them on her face during the collision.
b) During the collision, the girl’s face pushed the glasses forward.
c) The glasses continued moving forward because the force of the air on
them was less than the force of the girl’s face on them.
d) During the collision, the car pushed the girl forward causing her glasses
to fly off her face.
e) During the collision, the wall pushed the car backward and the girl
reacted by pushing her glasses forward.
Frame of Reference
 An inertial reference frame is one in which Newton’s
law of inertia is valid.
 All accelerating reference frames are non-inertial.
 We assume earth is an inertial reference frame
since the acceleration is small.
Question #4
a)
b)
c)
d)
e)
If an object is moving can you conclude there are forces acting
on it? If an object is at rest, can you conclude there are no
forces acting on it? Consider each of the following situations. In
which one of the following cases, if any, are there no forces
acting on the object?
A bolt that came loose from a satellite orbits the earth at a
constant speed.
After a gust of wind has blown through a tree, an apple falls to
the ground.
A man rests by leaning against a tall building in downtown
Dallas.
Sometime after her parachute opened, the sky diver fell toward
the ground at a constant velocity.
Forces are acting on all of the objects in choices a, b, c, and d.
Question #5
A child is driving a bumper car at an amusement park. During one
interval of the ride, she is traveling at the car’s maximum speed when
she crashes into a bumper attached to one of the side walls. During the
collision, her glasses fly forward from her face. Which of the following
statements best describes why the glasses flew from her face?
a) The glasses continued moving forward because there was too little
force acting on them to hold them on her face during the collision.
b) During the collision, the girl’s face pushed the glasses forward.
c) The glasses continued moving forward because the force of the air on
them was less than the force of the girl’s face on them.
d) During the collision, the car pushed the girl forward causing her glasses
to fly off her face.
e) During the collision, the wall pushed the car backward and the girl
reacted by pushing her glasses forward.
Chapter 4:
Forces and Newton’s Laws of Motion
Section 3:
Newton’s Second Law of Motion
Newton’s 2nd Law
 Quantifies the magnitude and direction of the accelerations.
 When a net force is present, the acceleration of the object is
proportional to the net force and inversely proportional to the
mass of the object.
 The direction of the acceleration is the same as the direction
of the net force.
 ac is the constant added that “fixes” the units.
 usually ignored/forgotten

a

F
m ac
F  F
net
 ma
SI Unit of Force
SI Unit for Force
kg  m
N 2
s
This combination of units is called a newton (N).
Working 2nd Law Problems
1. Identify the system being accelerated.
2. Define a coordinate system.
3. Identify forces by drawing a force or free body
diagram.
4. Explicitly write SF=ma
5. Replace SF with the actual forces in your free body
diagram.
6. Substitute numeric values, where appropriate, and
solve for unknowns.
Question #6
A car of mass m is moving at a speed 3v in the left
lane on a highway. In the right lane, a truck of mass
3m is moving at a speed v. As the car is passing
the truck, the driver notices that the traffic light
ahead has turned yellow. Both drivers apply the
brakes to stop ahead. What is the ratio of the force
required to stop the truck to that required to stop the
car? Assume each vehicle stops with a constant
deceleration and stops in the same distance x.
a) 1/9
b) 1/3
c) 1
e) 9
d) 3
Question #7
The graph shows the velocities of two objects as a function of
time. During the intervals A, B, and C indicated, net forces F A ,
F B , and FC act on the two objects, respectively. If the objects
have equal mass, which one of the following choices is the
correct relationship between the magnitudes of the three net
forces?
a) FA > FB = FC
b) FC > FA > FB
c) FA < FB < FC
d) FA = FB = FC
e) FA = FC > FB
Comparison of units
So, what’s all this mean?
A man stands on a scale
inside a stationary elevator.
Forces acting on the man
F  0
N  mg  0
N
N  mg
Reading
on scale
mg
And then…
When Moving Upward With
Constant Velocity
Forces acting on the man
 F  ma
a0
v
N
N  mg  m0
N  mg
Reading
on scale
mg
And then…
When Moving Upward With
Constant Acceleration
Forces acting on the man
 F  ma
N  mg  ma
a
N
N  mg  ma
N  mg  a 
Reading
on scale
mg
And then…
When Moving Downward With
Constant Acceleration
Forces acting on the man
 F  ma
mg  N  ma
a
N
N  mg  ma
N  mg  a 
Reading
on scale
mg
Chapter 4:
Forces and Newton’s Laws of Motion
Section 4:
The Vector Nature of Newton's Second
Law of Motion
Section 4-The short, short version
 Forces are a vector
 Just as with velocity, acceleration, Forces that are
perpendicular are independent of each other

F
y


F  ma
is equivalent to
 ma y
F
x
 max
Question #8
In a grocery store, you push a 14.5-kg cart with a
horizontal force of 12.0 N. If the cart starts at rest,
how far does it move in 3.00 seconds?
Question #9
A catcher stops a 92 mph pitch in his glove, bringing
it to rest in 0.15 m. If the force exerted by the
catcher is 803 N, what is the mass of the ball?
Chapter 4:
Forces and Newton’s Laws of Motion
Section 5:
Newton’s 3rd Law of Motion
Newton’s Third Law
 For every action there exists an equal and opposite
reaction.
 If A exerts a force F on B, then B exerts a force of -F
on A.
Example Problem:
You rest a book on a table.
a) Identify the forces acting on the book with a free
body diagram.
b) Are these forces equal and opposite?
c) Are these forces an action-reaction pair? Why or
why not?
Requirements for Newton’s Laws
 The 1st and 2nd laws require that ONE system be
analyzed and that ALL the forces on the system be
accounted for.
 The 3rd law requires that TWO systems be analyzed
and that the forces of interaction between the two be
accounted for.
Question #10
A water skier is being pulled by a rope attached to a
speed boat moving at a constant velocity. Consider the
following four forces: (1) the force of the boat pulling
the rope, (2) the force of the skier pulling on the rope,
(3) the force of the boat pushing the water, and (4) the
force of the water pushing on the boat. Which two
forces are an “action-reaction” pair that is consistent
with Newton’s third law of motion?
a) 1 and 2
b) 2 and 3
c) 2 and 4
d) 3 and 4
e) 1 and 4
Question #11
A large crate is lifted vertically at constant speed by a rope
attached to a helicopter. Consider the following four forces that
arise in this situation: (1) the weight of the helicopter, (2) the
weight of the crate, (3) the force of the crate pulling on the earth,
and (4) the force of the helicopter pulling on the rope. Which one
of the following relationships concerning the forces or their
magnitudes is correct?
a) The magnitude of force 4 is greater than that of force 2.
b) The magnitude of force 4 is greater than that of force 1.
c) Forces 3 and 4 are equal in magnitude, but oppositely directed.
d) Forces 2 and 4 are equal in magnitude, but oppositely directed.
e) The magnitude of force 1 is less than that of force 2.
Question #12
An astronaut is on a spacewalk outside her ship in “gravity-free” space.
Initially, the spacecraft and astronaut are at rest with respect to each
other. Then, the astronaut pushes to the left on the spacecraft and the
astronaut accelerates to the right. Which one of the following
statements concerning this situation is true?
a) The astronaut stops moving after she stops pushing on the
spacecraft.
b) The velocity of the astronaut increases while she is pushing on the
spacecraft.
c) The force exerted on the astronaut is larger than the force exerted
on the spacecraft.
d) The spacecraft does not move, but the astronaut moves to the right
with a constant speed.
e) The force exerted on the spacecraft is larger than the force exerted
on the astronaut.
Chapter 4:
Forces and Newton’s Laws of Motion
Section 6:
Types of Forces: An Overview
Two Types of Forces
 Fundamental Forces
Always present in nature
Gravitational, Strong Nuclear, Electroweak
 Non-fundamental Forces
Present in certain situations usually as a result of
Fundamental and applied forces.
Normal, Tension, Friction
Natural Forces
Types
Range
Size
Gravitational
Unlimited
100
Electromagnetic
Unlimited
106
Weak Nuclear
 1012 m
1020
Strong Nuclear
 1015 m
1035
Chapter 4:
Forces and Newton’s Laws of Motion
Section 7:
The Gravitational Force
Newton’s Law of Universal Gravitation
 Every particle in the universe exerts an attractive
force on every other particle.
 A particle is a piece of matter, small enough in size
to be regarded as a mathematical point.
 The force that each exerts on the other is directed
along the line joining the particles.
 For two particles that have masses m1 and m2 and
are separated by a distance r, the force has a
magnitude given by:
m1m2
F G 2
r
G  6.673 1011 N  m 2 kg 2
Weight
 The weight of an object on or above the earth is the
gravitational force that the earth exerts on the
object.
 The weight always acts downwards, toward the
center of the earth.
 On or above another astronomical body, the weight
is the gravitational force exerted on the object by
that body.
 SI Unit of Weight: newton (N)
Relation Between Mass and Weight
W G
M Em
r
W  mg
ME
g G 2
r
2
On the earth’s surface
ME
g G 2
RE

 6.67 10
 9.80 m s
11
2
N  m kg
2
 5.98 10 kg 
6.38 10 m
24
2
6
2
Question #13
A cannon fires a ball vertically upward from the Earth’s surface.
Which one of the following statements concerning the net force
acting on the ball at the top of its trajectory is correct?
a) The net force on the ball is instantaneously equal to zero
newtons at the top of the flight path.
b) The direction of the net force on the ball changes from upward
to downward.
c) The net force on the ball is less than the weight, but greater
than zero newtons.
d) The net force on the ball is greater than the weight of the ball.
e) The net force on the ball is equal to the weight of the ball.
Question #14
If an object at the surface of the Earth has a weight
W, what would be the weight of the object if it was
transported to the surface of a planet that is onesixth the mass of Earth and has a radius one third
that of Earth?
a) 3W
b) 4W/3
c) W
d) 3W/2
e) W/3
Question #15
Two objects that may be considered point masses are initially
separated by a distance d. The separation distance is then
decreased to d/3. How does the gravitational force between these
two objects change as a result of the decrease?
a) The force will not change since it is only dependent on the
masses of the objects.
b) The force will be nine times larger than the initial value.
c) The force will be three times larger than the initial value.
d) The force will be one third of the initial value.
e) The force will be one ninth of the initial value.
Chapter 4:
Forces and Newton’s Laws of Motion
Section 8:
The Normal Force
Definition of the Normal Force
 The normal force is one component of the force that
a surface exerts on an object with which it is in
contact – namely, the component that is
perpendicular to the surface.
Sample Problem
If you apply an 11 N force to a 15 N block which is
resting on a table, what is the normal force the table
exerts on the block?



SF  0  FN  FW  FA
FN  15 N  11 N  0
FN  26 N
Sample Problem
What is the normal force if instead of pushing down
on the 15 N block, you lift it with 11 N of force?



SF  0  FN  FW  FA
FN  15 N  11 N  0
FN  4 N
Apparent Weight
 What we feel as “our weight” is the normal force
acting on us.
Apparent Weight
F
y
  FN  mg  ma
FN  mg  ma
apparent
weight
true
weight
Question #16
A free-body diagram is shown for the following
situation: a force P pulls on a crate of mass m on a
rough surface. The diagram shows the magnitudes
and directions of the forces that act on the crate in this
situation. FN represents the normal force on the crate, g
represents the acceleration due to gravity, and f
represents the frictional force. Which one of the
following expressions is equal to the magnitude of the
normal force?
a) P  f / 
b) P  f
c) P  f  mg
e) zero
d) mg
Question #17
4.8.3. Consider the three cases shown in the drawing in which the same force F
is applied to a box of mass M. In which case(s) will the magnitude of the
normal force on the box equal (F sin  + Mg)?
a) Case One only
b) Case Two only
c) Case Three only
d) Cases One and Two only
e) Cases Two and Three only
Question #18
Consider the situation shown in the drawing. Block A has a mass 1.0
kg and block B has a mass 3.0 kg. The two blocks are connected by a
very light rope of negligible mass that passes over a pulley as shown.
The coefficient of kinetic friction for the blocks on the ramp is 0.33.
The ramp is angled at  = 45. At time t = 0 s, block A is released
with an initial speed of 6.0 m/s. What is the tension in the rope?
a) 11.8 N
b) 7.88 N
c) 15.8 N
d) 13.6 N
e) 9.80 N
Chapter 4:
Forces and Newton’s Laws of Motion
Section 9:
Static and Kinetic Friction Forces
Static and Kinetic Frictional Forces
When an object is in
contact with a surface
there is a force acting on
that object. The
component of this force
that is parallel to the
surface is called the
frictional force.
Static Friction
When the two surfaces
are not sliding across one
another the friction is
called static friction.
Static Friction
The magnitude of the static frictional force can have
any value from zero up to a maximum value.
fs  f
f
MAX
s
0  s  1
MAX
s
  s FN
is called the coefficient of static friction.
Static Friction
Note that the magnitude of the frictional force does
not depend on the contact area of the surfaces.
Static vs. Kinetic Friction
 Static friction opposes the impending relative motion
between two objects.
 Kinetic friction opposes the relative sliding motion
motions that actually does occur.
f k   k FN
0  s  1
is called the coefficient of kinetic friction.
Sample Problem
 If a 40 pound child is sledding on a level surface, what is the
frictional force if the coefficient of friction is 0.05?
f k   k FN   k mg

0.0540kg  9.80 m s
2
  20kg
Question #19
On a rainy evening, a truck is driving along a
straight, level road at 25 m/s. The driver panics
when a deer runs onto the road and locks the
wheels while braking. If the coefficient of friction for
the wheel/road interface is 0.68, how far does the
truck slide before it stops?
a) 55 m
b) 47 m
c) 41 m
d) 36 m
e) 32 m
Question #20
Three pine blocks, each with identical mass, are sitting on a rough surface as shown.
If the same horizontal force is applied to each block, which one of the following
statements is false?
a) The coefficient of kinetic friction is the same for all three blocks.
b) The magnitude of the force of kinetic friction is greater for block 3.
c) The normal force exerted by the surface is the same for all three blocks.
d) Block 3 has the greatest apparent area in contact with the surface.
e) If the horizontal force is the minimum to start block 1 moving, then that same force
could be used to start block 2 or block 3 moving.
Question #21
A 1.0-kg block is placed against a wall and is held
stationary by a force of 8.0 N applied at a 45° angle
as shown in the drawing. What is the magnitude of
the friction force?
a) 3.7 N
b) 4.1 N
c) 5.8 N
d) 7.0 N
e) 8.0 N
Chapter 4:
Forces and Newton’s Laws of Motion
Section 10:
The Tension Force
The Tension Force
 Cables and ropes transmit
forces through tension.
 A massless rope will
transmit tension
undiminished from one
end to the other.
 If the rope passes around
a massless, frictionless
pulley, the tension will be
transmitted to the other
end of the rope
undiminished.
Question #22
Some children are pulling on a rope that is raising a bucket via a
pulley up to their tree house. The bucket containing their lunch is
rising at a constant velocity. Ignoring the mass of the rope, but
not ignoring air resistance, which one of the following statements
concerning the tension in the rope is true?
a) The magnitude of the tension is zero newtons.
b) The direction of the tension is downward.
c) The magnitude of the tension is equal to that of the weight of
the bucket.
d) The magnitude of the tension is less than that of the weight of
the bucket.
e) The magnitude of the tension is greater than that of the weight
of the bucket.
Question #23
One end of a string is tied to a tree branch at a height h above the
ground. The other end of the string, which has a length L = h, is
tied to a rock. The rock is then dropped from the branch. Which
one of the following statements concerning the tension in the string
is true as the rock falls?
a) The tension is independent of the magnitude of the rock’s
acceleration.
b) The magnitude of the tension is equal to the weight of the rock.
c) The magnitude of the tension is less than the weight of the rock.
d) The magnitude of the tension is greater than the weight of the
rock.
e) The tension increases as the speed of the rock increases as it
falls.
Question #24
A rock is suspended from a string. Barbara accelerates the rock
upward with a constant acceleration by pulling on the other end of
the string. Which one of the following statements concerning the
tension in the string is true?
a) The tension is independent of the magnitude of the rock’s
acceleration.
b) The magnitude of the tension is equal to the weight of the rock.
c) The magnitude of the tension is less than the weight of the rock.
d) The magnitude of the tension is greater than the weight of the rock.
e) The tension decreases as the speed of the rock increases as it
rises.
Chapter 4:
Forces and Newton’s Laws of Motion
Section 11:
Equilibrium Applications of Newton’s Laws
of Motion
Definition of Equilibrium
 An object is in equilibrium when it has zero
acceleration.

Fx  0

Fy  0
Reasoning Strategy
 Select an object(s) to which the equations of
equilibrium are to be applied.
 Draw a free-body diagram for each object chosen
above.
 Include only forces acting on the object, not forces
the object exerts on its environment.
 Choose a set of x, y axes for each object and
resolve all forces in the free-body diagram into
components that point along these axes.
 Apply the equations and solve for the unknown
quantities.
Sample Problem
The picture below shows a traction device used with a foot
injury. The weight of the 2.2-kg object creates a tension in the
rope that passes around the pulleys. The foot pulley is kept in
equilibrium because the foot also applies a force to it. Ignoring
the weight of the foot, find the magnitude of the force F .
Solution:
SFy  0  T1 sin 35  T2 sin 35
T  mg
T1  T2  T
SFx  0  T cos 35  T cos 35  F
F  2T cos 35

F  22.2 kg 9.80 m s
F  35 N
2
cos 35
Question #25
Consider the following: (i) the book is at rest, (ii) the
book is moving at a constant velocity, (iii) the book is
moving with a constant acceleration. Under which
of these conditions is the book in equilibrium?
a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii) only
e) (ii) and (iii) only
Question #26
A block of mass M is hung by ropes as shown. The system is
in equilibrium. The point O represents the knot, the junction of
the three ropes. Which of the following statements is true
concerning the magnitudes of the three forces in equilibrium?
a) F1 + F2 = F3
b) F1 = F2 = 0.5×F3
c) F1 = F2 = F3
d) F1 > F3
e) F2 < F3
Question #27
A team of dogs pulls a sled of mass 2m with a force P. A second
sled of mass m is attached by a rope and pulled behind the first
sled. The tension in the rope is T. Assuming frictional forces are
too small to consider, determine the ratio of the magnitudes of the
forces P and T , that is, P/T.
a) 3
b) 2
c) 1
d) 0.5
e) 0.33
Chapter 4:
Forces and Newton’s Laws of Motion
Section 12:
Non-equilibrium Applications of Newton’s
Laws of Motion
Nonequilibrium Application of
Newton’s Laws of Motion
 When an object is accelerating, it is not in
equilibrium.
F
x

 max
Fy  may
Example 14 Towing a Supertanker
A supertanker of mass m = 1.50 × 108 kg is being
towed by two tugboats. The tensions in the towing
cables apply forces at equal angles of 30.0° with
respect to the tanker's axis. In addition, the tanker's
engines produce a forward drive force, whose
magnitude is D = 75.0 × 103 N. Moreover, the water
applies an opposing force, whose magnitude is R =
40.0 × 103 N. The tanker moves forward with an
acceleration that points along the tanker's axis and
has a magnitude of 2.00 × 10-3 m/s2. Find the
magnitudes of the tensions.
The acceleration is along the x axis so
ay  0
Force

T1

T2

D

R
x component
y component
 T1 cos 30.0
 T2 cos 30.0

 T1 sin 30.0

 T2 sin 30.0
D
0
R
0


F
y
  T1 sin 30.0  T2 sin 30.0  0

 T1  T2
F
x
 max
  T1 cos 30.0  T2 cos 30.0  D  R

T1  T2  T
max  R  D
5
T
 1.53 10 N

2 cos 30.0
Question #28
A constant force F acts on a block of mass m. which is initially
at rest. Find the velocity of the block after time Dt.
F
vo = 0
Dt = 5 s
v =?
m
F  ma
F = 20 N
m = 5 kg
Dv
a
Dt
 v  vo 
 Dv 
F  m   m 

 Dt 
 Δt 
FDt
v
m
20 N5 s 

5 kg
 20 m/s
Question #29
A force of magnitude F pushes a block of mass 2m,
which in turn pushes a block of mass m as shown.
The blocks are accelerated across a horizontal,
frictionless surface. What is the magnitude of the
force that the smaller block exerts on the larger
block?
a) F/3
b) F/2
c) F
d) 2F
e) 3F