newton’s laws of motion - sfsu physics & astronomywman/phy111hw/lecture notes...your dog...
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Units of Chapter 5
• Force and Mass
• Newton’s First Law of Motion
• Newton’s Second Law of Motion
• Newton’s Third Law of Motion
• The Vector Nature of Forces
• Normal Force, Tension,
• Free body diagram, Problem solving skills
• Weight, Apparent weight 2
5-1 Force and Mass
Mass is the measure of
how hard it is to
change an object’s
velocity.
Mass can also be
thought of as a
measure of the quantity
of matter in an object.
The more matter one
object has, the harder it
is to change its
velocity. 4
5-2 Newton’s First Law of Motion
If you stop pushing an object, does it stop
moving?
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Only if there is friction! In the absence of any net
external force, an object will keep moving at a
constant speed in a straight line, or remain at rest.
This is also known as the Law of Inertia.
If the net force on an object is zero, it’s velocity is
constant (a=0). INERTIA (need safety belt)
Attention: If there is friction, Air resistance… net
force is not zero.)
In order to change the velocity of an object ,
magnitude or direction , a net force is required.
Example: Object on desk.
Net force =_____
5-2 Newton’s First Law of Motion
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Objects want to keep doing what they are already
doing.
For example:
in space…
Movie Unstoppable
Your dog knows…
5-3 Newton’s Second Law of Motion
If net force is not zero, velocity will not be constant.
a≠0
Object’s acceleration will be in the same directions
as the net force.
Acceleration direction is not the velocity direction.
Acceleration direction determines velocity change.
Fnet = ma
Acceleration is proportional to net force.
The more net force, the larger the acceleration. 7
5-3 Newton’s Second Law of Motion
Fnet = ma
Acceleration is inversely proportional to mass:
Same Force, less mass object gets bigger a.
Same Force, more mass object gets smaller a.
More mass, more inertia, harder to change v, less a
Less mass, less inertia, easier to change v, more a
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5-3 Newton’s Second Law of Motion
An object may have several forces acting on it;
the acceleration is due to the net force:
(5-1)
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SI unit for forces: Newton, (N)
F= m a; 1 Newton of net force gives 1 kg mass
1m/s2 acceleration.
1 N = 1 kg * m/s2
Attention: when you solve problem, if you first
convert every value to standard SI unit.
(m, s, m/s, m/s2 , N, ….) you can plug the numbers
and automatically get SI unit in your answer.
In order to give object of mass m a downward
acceleration of g=9.8 m/s2, how much force is
needed?
Gravity force = m g 10
Weight
The weight of an object on the Earth’s surface is
the gravitational force exerted on it by the Earth.
, also known as Gravity, G
G=mg
1 kg mass weights 9.8 Newton on earth.
9.8 Newton gravity force gives 1kg mass an
acceleration of 9.8m/s211
5-4 Newton’s Third Law of Motion
Forces always come in pairs.
If object A exerts a force “F” on object B (action)
then object B must exert a force “negative F” on
object A (reaction).
Action and reaction forces are always
equal in size and opposite in directions.
Action /Reaction pair examples:
I push you, I feel your resistant.
These two forces are always equal and opposite(Will you push a nail tip or blade with large force?
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The 3rd law of Newton’s law is about two objects !
Not one object!
No, because the reaction resistant force from the blade
is as big as the push you give to it)
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Newton’s 3rd law applications:
1.
2. Throw heavy object forward. You feel recoil backward.
3. Swim, push water back, so that you can move
forward (water’s reaction force on you is forward)
4. Walk/run, you need to press down and back, so that
floor’s reaction force is upward and forward.
(That’s why on ice and sand it’s so hard to walk or drive)
5, Water hose sneak around….
6, Air balloon flies upward, while gas in it was squeezed
downward. (demo)
7, Your gravity, you 100 kg earth act 980 N gravity
force on you downward.
You act 980 N, gravity force on Earth upward.
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These two forces are not action and reaction pair:
I push you on left side.
He push you on your right side.
On one object bearing two forces.
These two forces are not action and reaction.
They can be equal or not. Nobody guarantee these
two forces to be equal.
I push you and you resist me, these two forces are
action and reaction pair. Newton’s 3rd law guarantee
these two forces to be equal in side and opposite in
directions.
These is very useful for calculations.
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These two forces are two forces acting on one object.
These two forces can be equal or not.
Free-body diagrams:
A free-body diagram shows every force acting on
an object.-Use a dot to represent the object of interest.
-Use one arrow with correct length and direction
to represent each force.
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Exercise for yourself: Forces add as vectors.
A hockey puck is acted on
by one or more forces, as
shown in Figure 5-19.
Rank the four cases, A, B,
C, and D, in order of the
magnitude of the puck's
acceleration, starting with
the smallest. Indicate ties
with an equal sign. (Use
only the symbols < and =,
for example A < B=C.) A < D < B < C
5-5 The Vector Nature of Forces: Forces in
Two Dimensions
The easiest way to handle forces in two
dimensions is to treat each dimension
separately, as we did for kinematics.
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The normal force is
the force exerted by
a surface on an
object.
Very often it is a
supporting force.
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5-7 Special forces, Normal Forces
5-7 Special forces, Normal Forces
Normal force is the force from a surface. Label N.
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Direction: Always perpendicular
& away from surface.
Size : depend on press of object.
How much you press, how much
It supports.
The normal force
may be equal to,
greater than, or less
than the weight.
When you pull on a string or rope, it becomes
taut. We say that there is tension in the string.
Special forces, Tension, Lable T
Direction: Always along rope,
always pointing away from
Object.
Size :
Tension inside
massless rope
in all location
has the
same size.
6-2 Strings and Springs
The tension in a real rope will vary along its
length, due to the weight of the rope.
Here, we will assume that
all ropes, strings, wires,
etc. are massless unless
otherwise stated.
Tension inside massless
rope in all location
has the same size.
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** problem solving strategy and steps
This is the most important slides for this semester.
1, Identify and isolate the object of interest, a dot.
2, Identify all forces on the object acted by
other objects. Label them using arrows of correct
length and direction
3, Pick x – y axis. ( based on acceleration
direction for convenience)
4, Break up all forces into x-y components
5, Set equations:
Add all force components in x directions = max
Add all force components in y directions = may
Fnet x= m ax , Fnet y= m ay (x & y are independent )
6, Solve for any two unknowns, from the above two
equations. (If know a, can solve force. If know forces
can find a. Again Math skills here. )
6-3 Translational Equilibrium
When an object is in translational equilibrium,
(Not moving or moving at constant velocity.)
the net force on it is zero:
This allows the calculation of unknown forces.
Add all force components in x directions = 0
Add all force components in y directions = 0
The traffic light problem.
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Example 1An object of mass m being dragged
with force F at angle q. (know m, F, q)
Find Normal force N, and acceleration.
1- object m, use a dot
2- label all forces on it mg, N, F
3- pick axes
4- components. F both x & y direction.
x direction: Fx component: Positive
y direction: Fy component: Positive
Fx= +Fcosq Fy = +Fsinq
5- Total F=ma for both x & y directions
+ or -?
Fnet x : Fcos θ =m ax,
Fnet y : N+Fsinθ-mg =may= 0
6- solve ax :
solve N :
ax =Fcos θ / m
N = mg - Fsinθ
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Example 2Incline plane. No friction.
We know m and angle q,
Find acceleration, and N.
1, object: dot
2, forces: mg, N, anything else?
3, pick x-y axes cleverly. (Along motion direction,
So that we know for sure ay=0)
4, force components: weight along incline: mgsinq
weight perpendicular to incline: mgcosq
It’s very important to do the drawing yourself.
5, Total F=ma; x direction : mgsinq =max
y direction: N-mgcosq=0
6, solve equations: ax=gsinq; N=mgcosq; Check for special angles. If q=0, a=0, N=mg; If q=90, a=g, N=0,
Make sense. Large q, Larger sinq, Larger a, smaller q, Less N
5-6 Apparent Weight
Apparent weight: Your perception of your weight is
based on the contact forces between your body
and your surroundings. It’s N or T…
If you are accelerating
your surroundings , your
apparent weight may be
more or less than your
actual weight.
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If Accelerating downward,
Define downward to be positive direction:
mg-N=may ; so N= mg- may
N<mg, you still has same mg, but no enough support.
That’s what frightens you badly in those terror rides.
Apparent weight =N <mg,
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If acceleration is downward,
Mass unchanged. Gravity unchanged.
But Normal force is less. Apparent weight is less.This is what frightens you in the theme park rides.
Even in complete dark, you can tell N<mg, feel downward a
In an elevator, that is accelerating upward:
N>mg , N - mg = m|ay|; N= mg + m|ay|) > mg
Mass unchanged, gravity unchanged,
But apparent weight is more!Look at the poor girl.
T= mg + m|ay|, when a is upward
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If no elevator, try quickly stand up or squat on scale.
Acceleration is not equal to 0 (Try it at home)
This is how Wii fit detect your motion (acceleration)
by measuring the Normal forces between it and you.
________________________________________Question, in an elevator, going down at constant velocity
N > = < mg???? a=????
Answer: a= 0; N = mg
Q: Constant velocity elevator going up ?
Apparent weight, N= ??
Before next class, at least Read Chapter 6-1 friction,
Summary of Chapter 5• Force: a push or pull
• Mass: measures the difficulty in accelerating an
object
• Newton’s first law: if the net force on an object
is zero, it stay at rest or keep constant velocity.
•Newton’s second law: for one object
• Free-body diagram: a sketch showing all the
forces on an object. Remember to decompose in
x and y directions.
•Solve F=ma in both x and y direction separately
Add all forces in x directions = max
Add all forces in y directions = may
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Summary of Chapter 5
• Newton’s third law: If object 1 exerts a force
F on object 2, then object 2 exerts a force –F
on object 1.
• Contact forces: an action-reaction pair of
forces produced by two objects in physical
contact
• Forces are vectors
• Newton’s second laws can be applied to x
and y each components of the forces
separately
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Summary of Chapter 5
• Weight: gravitational force exerted by the Earth on
an object, Always DOWNWARD.
•On the surface of the Earth, W = mg
• Apparent weight: force felt from contact with a floor
or scale. It’s determined by both mg and acceleration
• Normal force: Always perpendicular to the surface.
(away from the surface)
• Normal force is determined by the amount of
“pressing” again the surface. It may be equal to,
lesser than, or greater than the object’s weight.
• Tension force in a string is always ALONG the string.
It is equal everywhere if the string has no mass. 34