Force

1
Force
A force is a push or pull. An object at rest
needs a force to get it moving a moving object
needs a force to change its velocity.
The magnitude of a force can be measured using a
spring scale.
2
Newton vs. Galileo

• Newton needs to supplant Galileos ideas by
  redefining some terms that Galileo used and
  creating definitions for terms that Galileo
  didnt define
• That doesnt mean Galileo was wrong! Just that
  Newton finds his definitions incomplete for
  placing motion into a bigger, more complete
  picture

3
Newtons First Law of Motion
Newtons first law is often called the law of
inertia. Every object continues in its state of
rest, or of uniform velocity in a straight line,
as long as no net force acts on it.
4
Mass
Newtons genius the operational
definition Define something by stating what it
does, not what it is!
Mass is the measure of inertia of an object. In
the SI system, mass is measured in
kilograms. Mass is not weight Mass is a property
of an object. Weight is the force exerted on that
object by gravity. If you go to the moon, whose
gravitational acceleration is about 1/6 g, you
will weigh much less. Your mass, however, will be
the same.
5
Newtons Second Law of Motion
Newtons second law is the relation between
acceleration and force. Acceleration is
proportional to force and inversely proportional
to mass. If theres no force, theres no
acceleration! If theres no mass, theres no net
force!
Important point force and mass are intimately
related and can be operationally defined only in
terms of each other!
6
Concep Question 1
7
Concep Question 1
There are forces acting on the book, but the only
forces acting are in the vertical direction.
Gravity acts downward, but the table exerts an
upward force that is equally strong, so the two
forces cancel, leaving no net force.
8
Concep Question 2
1) a net force acted on it 2) no net force
acted on it at all 3) the book remained at
rest 4) it didnt move, it only seemed to 5)
its something to do with gravity
You put your physics book on the car seat next to
you. When the car stops suddenly, the book
slides forward off the seat. Why?
9
Concep Question 2
1) a net force acted on it 2) no net force
acted on it at all 3) the book remained at
rest 4) it didnt move, it only seemed to 5)
its something to do with gravity
You put your physics book on the car seat next to
you. When the car stops suddenly, the book
slides forward off the seat. Why?
The book was initially moving forward (since it
was in moving car). When the car stopped, the
book continued moving forward, which was its
initial motion. It therefore slides forward with
respect to the car. If we ignore friction, there
is no net force on the book.
10
Concep Question 3
1) the force pushing the stone forward finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of steam 5)
the stone has a natural tendency to be at rest
1) the force pushing the stone finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of
steam 5) the stone has a natural tendency
to be at rest
You kick a smooth flat stone out on a frozen
pond. The stone slides, slows down and
eventually stops. You conclude that
11
Concep Question 3
1) the force pushing the stone finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of
steam 5) the stone has a natural tendency to
be at rest
You kick a smooth flat stone out on a frozen
pond. The stone slides, slows down and
eventually stops. You conclude that
Gravity acts only in the vertical direction but
the motion is in the horizontal direction. There
is nothing other than the ice to interact with
the puck, so the ice must be acting on the puck
to slow it. The force is small compared to the
pucks inertia but present nonetheless. We
attribute this to friction.
12
Concep Question 4
1) the force pushing the stone forward finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of steam 5)
the stone has a natural tendency to be at rest
1) the top string breaks 2) the bottom string
breaks 3) both strings break 4) Impossible to
tell without specifying how the pull is
done 5) whaaat???
A box hangs from the ceiling by a thread. A
second string is attached to the bottom of the
box. If you pull sufficiently hard on the bottom
string, what happens?
F
13
Concep Question 4
A box hangs from the ceiling by a thread. A
second string is attached to the bottom of the
box. If you pull sufficiently hard on the bottom
string, what happens?
1) the top string breaks 2) the bottom string
breaks 3) both strings break 4) Impossible to
tell without specifying how the pull is
done 5) whaaat???
Because of inertia, it does depend on how you did
the pull. A sharp pull is resisted by the box
(which has tension applied to it by the string)
and thus the bottom string breaks. A slow pull
allows the box to transmit all the tension plus
its weight to the top string so the top string
breaks.
14
Newtons Second Law of Motion
Force is a vector, i.e. like velocity and
acceleration, you need to specify its magnitude
and direction, so is true
along each coordinate axis.
The unit of force in the SI system is the newton
(N). Note that the pound is a unit of force, not
of mass, and can therefore be equated to newtons
but not to kilograms.
15
Concep Question 5
1) the force pushing the stone forward finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of steam 5)
the stone has a natural tendency to be at rest
A force F acts on a mass m1 giving acceleration
a1. The same force acts on a different mass m2
giving acceleration a2 2a1. If m1 and m2 are
glued together and the same force F acts on this
combination, what is the resulting acceleration?
1) ¾ a1 2) a1 3) ½ a1 4) a1 5)
a1
m1
a1
F m1 a1
F
m2
a2 2a1
F
m2
m1
a3
F
a3 (?) a1
16
Concep Question 5
1) the force pushing the stone forward finally
stopped pushing on it 2) no net force acted on
the stone 3) a net force acted on it all
along 4) the stone simply ran out of steam 5)
the stone has a natural tendency to be at rest
A force F acts on a mass m1 giving acceleration
a1. The same force acts on a different mass m2
giving acceleration a2 2a1. If m1 and m2 are
glued together and the same force F acts on this
combination, what is the resulting acceleration?
1) ¾ a1 2) a1 3) ½ a1 4) a1 5)
a1
m1
a1
F m1 a1
F
Mass m2 must be (1/2)m1 because its acceleration
was 2a1 with the same force. Adding the two
masses together gives (3/2)m1, leading to an
acceleration of (2/3)a1 for the same applied
force.
m2
a2 2a1
F
m2
m1
a3
F
F (3/2)m1 a3 gt a3 (2/3) a1
17
Weight the Force of Gravity and the Normal
Force
Weight is the force exerted on an object by
gravity. Close to the surface of the Earth, where
the gravitational force is nearly constant, the
weight is
18
Concep Question 6
1) Fg is greater on the feather 2) Fg is
greater on the stone 3) Fg is zero on both due
to vacuum 4) Fg is equal on both always 5) Fg
is zero on both always
What can you sayabout the force of gravity Fg
acting on a stone and a feather in a vacuum tube?
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Concep Question 6
1) Fg is greater on the feather 2) Fg is
greater on the stone 3) Fg is zero on both due
to vacuum 4) Fg is equal on both always 5) Fg
is zero on both always
What can you sayabout the force of gravity Fg
acting on a stone and a feather in a vacuum tube?
The force of gravity (weight) depends on the mass
of the object!! The stone has more mass,
therefore more weight.
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Why Do We Do Force Problems?

• All science is either physics or stamp
  collecting. E. Rutherford
• Nature and nature's laws lay hid in nightGod
  said 'Let Newton be' and all was light. A.
  Pope
• Start by doing what's necessary, then do what's
  possible, and suddenly you are doing the
  impossible. St. Francis of Assisi

21
Newtons Third Law of Motion
Any time a force is exerted on an object, that
force is caused by another object. Newtons third
law Whenever one object exerts a force on a
second object, the second exerts an equal
magnitude force in the opposite direction on the
first.
These are not the same forces as they act on
different objects, but they do have the same
magnitude
22
Newtons Third Law of Motion
A key to the correct application of the third law
is that the forces are exerted on different
objects. Make sure you dont use them as if they
were acting on the same object.
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Weight the Force of Gravity and the Normal
Force
An object at rest must have no net force on it.
If it is sitting on a table, the force of gravity
is still there what other force is there? The
force exerted perpendicular to a surface is
called the normal force. It is exactly as large
as needed to balance the force from the object
(if the required force gets too big, something
breaks!)
24
Tension and Pulleys
Pulleys are a tool which gives a decided
advantage in moving objects they allow you to
multiply the effect of a tension force. We assume
here only ideal pulleys and ideal strings ideal
pulleys are massless and frictionless ideal
strings are massless and stretchless.
The tension in a continuous string has the same
magnitude throughout the string!
T
T
m1
m2
m1 g
m2 g
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Newtons Third Law of Motion
Rocket propulsion can also be explained using
Newtons third law hot gases from combustion
spew out of the tail of the rocket at high
speeds. The reaction force is what propels the
rocket.
Note that the rocket does not need anything to
push against.
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Newtons Third Law of Motion
Helpful notation the first subscript is the
object that the force is being exerted on the
second is the source.
This need not be done indefinitely, but is a good
idea until you get used to dealing with these
forces.
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