Download Unit 2 Newton

Newton's Laws of Motion
Newton's First Law
A force is a push or a pull. The source may be gravitational,
electrical, magnetic, pulling on a rope, a contact force
between two objects that touch, etc. Common units of force
are the Newton (N) and the pound (lb) (9.8 N = 2.2 lb). One
Newton is equivalent to 1 kg·m/s2.
"Every object continues in its state of rest, or in its state of
uniform motion in a straight line at constant speed, unless it is
compelled to change that state by an external net force."
Newton's first law is sometimes called the law of inertia.
Inertia is the tendency of things to resist change in motion.
9.8 N
1 kg
For example, the force of gravitational
attraction of an object here on the Earth is
called its weight. It is proportional to the
mass of the object and can be written as
W=mg. Note that the weight of the object
is still mg even if it is not accelerating.
Mass is a measure of the quantity of matter. It is also a
measure of inertia or the sluggishness that an object exhibits
in response to any effort made to start it, stop it, or change
its state of motion in any way.
When you hit a volleyball, it might hurt as the ball bounces
off your arm to go sailing over the net. That's because the
mass of the ball makes it resist your effort to change its
state of motion. Bowling balls, on the other hand, have much
more mass than volleyballs. If you tried to knock a bowling
ball over the net, you just might break your arm!
Is it harder to change the state
of motion of a truck or of a car?
The downward motion and sudden stopping of the
bottle will get you some ketchup on your fries. Why?
Net Force
Note that
force has both
a magnitude
(amount) and a
direction.
A rocket has a weight of 10,000 N and develops
50,000 N of upward thrust. What is the net force on
the rocket? Specify both the magnitude and direction.
Acceleration is a measure of the change in the state of
motion of an object.
2.1
PHYS 1010Q
© D.S. Hamilton
Newton's Second Law
2.2
PHYS 1010Q
Free fall revisited
"The acceleration of an object is equal to the net force acting
on the object divided by its mass. The direction of the
acceleration is in the direction of the net force."
The acceleration increases with increasing
force but decreases with increasing mass.
© D.S. Hamilton
A boulder is many times heavier
than a pebble — that is, the
gravitational force that acts on a
boulder is many times larger than
the gravitational force on the
pebble. Yet if you drop a boulder
and a pebble at the same time,
they will fall together with the
same acceleration. Why?
Let’s use Newton’s second law to find the acceleration of an
object when the net force on it is just its weight.
F
a = net
m
What is the acceleration of a 1000-kg car if the net force
on it is 3000 N?
W
Start with drawing a force diagram that shows the
object and all of the forces on it. We will choose
the positive direction to be down. In this example,
there is just the single force, W = mg.
From the diagram we see that the net force is Fnet = W (= mg)
Substitute this into Newton's 2nd law;
What is the acceleration of a 2000-kg
plane if the drag force and the thrust are
equal in size?
Fnet
m
mg
a=
m
a=g
a=
Using Newton’s 2nd law and the assumptions of free-fall, we
are able to calculate Galileo's experimental result.
2.3
PHYS 1010Q
© D.S. Hamilton
2.4
PHYS 1010Q
© D.S. Hamilton
Nonfree fall
Terminal velocity
If there is appreciable air drag on a falling object,
you should include the drag or resistance force into
your expression for the net force.
D
Fnet = mg - D
The value of D depends on the size and shape of
the object (ie on the amount of air the object
must plow through as it falls) and on the speed of
the falling object (the greater the speed, the
more air molecules it encounters per second and
thus the greater the force of molecular impact).
Consider a 80-kg skydiver who jumps out of a helicopter.
As the skydiver falls from rest, the downward velocity
increases which causes an increase in the upward drag force.
Find the acceleration at each of the four positions shown in
the diagram.
D=0N
W=mg
A skydiver with a mass of 80 kg is accelerating (downward)
at 4 m/s2. What is the force of air resistance (D) acting on
the skydiver?
D=200N
D=600N
D=800N
Use Newton's 2nd law to show that the acceleration of the
skydiver is a = g - D/m.
Once the acceleration reaches zero, the velocity becomes
constant. This constant final velocity is called the terminal
velocity.
2.5
Friction
PHYS 1010Q
© D.S. Hamilton
When two surface are in contact, a force of
friction can be present. If the two surfaces
are in relative motion, we have "sliding
friction". The frictional force is always
opposite to the direction of motion.
2.6
PHYS 1010Q
© D.S. Hamilton
Describe the reaction force in the following examples.
A crate has a mass of 20 kg. What applied “push” force is
required to produce an acceleration of 0.5 m/s2 if the
frictional force is known to be 25 N?
Newton's Third Law
"Whenever one object exerts a force on a second object, the
second object exerts an equal and opposite force back on the
first." One force is called the action force and the other the
reaction force. They are pairs of a single interaction and
neither force exits without the other. Note the action and
reaction forces act on different objects and not on the same
object.
In the interaction between the hammer
and the stake, the force that the hammer
exerts on the stake is equal in magnitude
and opposite in direction to the force that
the stake exerts on the hammer.
2.7
PHYS 1010Q
© D.S. Hamilton
When the cannon is fired, the force exerted
by the cannon on the ball is as large as the
reaction force exerted by the ball on the cannon. Hence the
cannon has a backwards "kick“.
Since the two forces are equal in magnitude, why doesn't
the cannon recoil with the same acceleration as the ball?
Does the earth really
accelerate towards the ball?
2.8
PHYS 1010Q
© D.S. Hamilton
Is it the Third Law or the Second Law?
A man with a mass of 60 kg is standing on his
bathroom scales. There are two forces on the
man, his weight W (the downward gravitational
force on him) which is equal in magnitude to the
upward force exerted on him by the scales, Fs.
Are these two equal and opposite forces
(W and Fs) action-reaction pairs?
Now suppose he is standing on the scales while riding in an
elevator that is accelerating upward at 2 m/s2. How much
force is being exerted on him by the scales?
2.9
PHYS 1010Q
© D.S. Hamilton