Download Class Notes Forces

Newton’s Laws of Motion
Objectives: After reading this section you will be able to
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Explain the motion of an object using Newton’s Laws.
Define inertia and provide examples of this property of matter.
Define the net force and show how forces can be added together to cause
or prevent motion.
Identify action and reaction force pairs.
define friction
distinguish between static and kinetic friction
calculate the force of friction given the weight and coefficient of friction
Newton’s Laws of Motion
In science, a hypothesis is an educated guess which is demonstrated by
experiments. When a hypothesis has been tested over and over again and has
not been contradicted, it may become known as a law or a principle. Isaac
Newton is credited for describing the rules that explain the motion of most
objects. Newton 's Laws of Motion govern nearly all of the mechanical motion
that we experience on Earth.
Inertia
Law 1: Every material object continues in its state of rest, or of uniform
motion in a straight line, unless it is compelled to change that state by
forces acting on it.
The 1st Law of Motion states that, "An object in motion tends to remain in motion
until acted upon by an outside force". This law also says that an object at rest will
remain at rest until acted upon by an outside force. Whatever an object is doing,
it tends to remain doing so, until acted upon by an outside force. Basically this
law says that an object tends to resist change, and this is the meaning of the
word inertia. Thus, the 1st law of motion is also known as the law of inertia. Inertia
is proportional to an objects mass, so the greater the mass, the greater the
inertia. In other words, mass is a measure of an object’s inertia - its ability to
resist changes in its state of motion.
Figure 1 - An elephant has a lot of mass and therefore a lot of inertia!
Example
If I slide a pencil across the floor, it is going to keep moving in a straight line until
acted upon by and outside force. So what might this force be? Well there is a
frictional force between the floor and the pencil. The pencil could collide with
another object or with a wall and come to rest. From another angle the 1st law of
motion is experienced when we try to push a heavy object such as a stalled car.
At first it is difficult to get an object going, however, once going, it is sometimes
difficult to stop it.
Tutorial - Newton's First Law
Forces
Law 2: The acceleration of an object is directly proportional to the net force
acting on the object, is in the direction of the net force, and is inversely
proportional to the mass of the object.
A force is simply a push or a pull. A force that acts on an object will cause it to
change its state of motion. Gravity is a force, which can cause an object to
accelerate toward the Earth. Newton's 2nd Law of Motion states that, "A net force
acting on a mass produces acceleration". This law is most commonly
remembered by the equation:
F = ma
Forces are measured in Newtons. 1 Newton is the amount of force needed to
accelerate a mass of 1 kg at a rate of 1 m/s/s.
Figure 2 - the acceleration of gravity is the constant ratio of force and mass
Forces are also vector quantities, as they have both a size and a direction.
Example
If a force of 10 Newtons [South] is applied to a bowling ball with a mass of 2 kg,
what will its acceleration be?
F = 10 N [S]
m = 2 kg
F = ma, or a = F/m = 10N[S] / 2 kg = 5 m/s/s [South]
Mass is not Weight
As we have seen, mass is a measure of an object's inertia. Mass is the same
everywhere. Weight, however, is a measure of the force of gravity acting on an
object. An object's weight will change as a result of its position in a gravitational
field. On the moon your mass will be the same, but your weight will be only 1/6 th
as large as on Earth.
Net Forces
The net force acting on an object is the sum of all the forces acting on an object.
If two people push in the same direction on a stalled car, each with a force of 25
Newtons, the net force will be 50 Newtons. In a tug of war competition
If the net force acting on an object is zero (Fn = 0), The object exists in a state of
equilibrium and only one of two conditions is possible.
1. The object is at rest or
2. The object is moving at constant velocity.
Both conditions represent a state of equilibrium. Thus, when solving problems
look for the words "at rest" or "constant velocity" and you can be sure that all the
forces are equal.
If the net force acting on an object is not zero (Fn ≠ 0), The object is accelerating
(or decelerating). Thus, when solving problems look to see if a net force is
present and if so, there must be acceleration, because the forces are
unbalanced.
Examples
1. What force would be required to accelerate a 100 kg bicycle at a rate of 5
m/s/s?
Mass = m = 100 kg
Acceleration = a = 5 m/s/s [Forward]
F= ma = (100 kg)(5 m/s/s)
F= 500 kg m/s/s = 500 Newtons
2. If I push on a box with a force of 10 Newtons [East] and you push with 15Newtons due west, the box will have a net force of 5-Newtons to the west. This
net force of 5-Newtons due west will cause the block to accelerate in the same
direction. (Remember both force and acceleration are vectors and both will act in
the same direction.)
3. If a sky diver has a mass of 50kg, then the force of gravity pulling him toward
the Earth will be 500 Newtons [Down]. If the force of air resistance pushing
upward on the sky diver is 300 Newtons [Up], what will be the net force on the
sky diver, and what will his acceleration be?
Remember the net force is the sum of the forces. The two forces acting on the
sky diver are acting in opposite directions.
500 N [Down] + 300 N [Up] = 200 N [Down]
So, the net force is 200 N [Down]
The acceleration of the sky diver will be the net force divided by the mass
a = 200 N[Down] / 50 kg = 4 m/s/s [Down]
Notice this actual acceleration is less than the theoretical value for
the acceleration of gravity (g) of 10 m/s/s.
When applying Newton's second law, remember that the greater the net force,
the greater the acceleration. Force is directly proportional to acceleration. Mass
is inversely proportional to acceleration.
Tutorial - Newton's Second Law
Free Body Diagrams
A free body diagram is a way of representing all the forces on an object without
the object being present. A book at rest on a table top will have two force acting
on it: Gravity is pulling the book down, and the table is pushing back on the book
upward. The support force of the table pushing up on the book is called the
normal force (FNormal). These two forces must be equal, and cancel each other,
because the book is not accelerating. In this case, the net force acting on the
book is zero (FNET = 0).
Figure 3 - Free body diagram of a book resting on a table top. The two forces
acting on the book are shown with arrows.
If the object is at rest and has a horizontal force of 20N to the right, friction will
oppose this force with 20N to the left. But both forces would be the same. Now
let's consider that the object is moving with a constant velocity toward the right.
Again the frictional force would oppose this motion with a force directed toward
the left. And once again the forces are equal, because constant velocity is
another state of equilibrium.
Tutorial - Drawing Free Body Diagrams
PhET Simulation - Forces in One Dimension
Action and Reaction
Law 3: Whenever one object exerts a force on a second object, the second
object exerts an equal and opposite force on the first.
Newton's 3rd law is commonly written "for every action there is an equal and
opposite reaction". This law can be tricky, because it easy to confuse action and
reaction forces with causes and effects. Action and reaction forces are
interactions. They occur at the same time (simultaneously) and one would not
exist without the other. Use the sentences below to describe action and reaction
force pairs:
Object A pushes on object B
Object B pushes back on object A with a force equal in size and opposite in
direction.
For example, when you blow up a balloon and then let go of the end it will fly
across the room. The motion of the balloon can be explained using action and
reaction forces. The balloon is stretched and it pushes on the air inside the
balloon. When the balloon is released, the balloon pushes the air out of the open
end. The air pushes back on the balloon, causing it to acceleration in the
opposite direction.
The balloon pushes on the air
The air pushes back on the balloon with a force equal in size and opposite
in direction
The amount of acceleration an object will experience will depend on both the
force and the mass. So, when a baseball bat hits a baseball, the force of the bat
on the ball is equal to the force of the ball on the bat. The ball will accelerate
much more, because it has less mass, and because you are holding on the bat
(preventing it from accelerating). Identifying and explaining action and reaction
forces can be tricky because there are often many different forces present in a
system. It is important to learn how to identify and label all the forces at work.
Figure 4 - Action and reaction force pairs shown for a car tire and the
road, a rocket and the combustion of the rocket fuel, a man pulling on a spring
attached to a wall, and a ball falling from the side of a building.
Tutorial - Newton's Third Law
Another look at Action and Reaction....
The Bug on the Windshield
Action and reaction forces can be among the hardest concepts in physics. The
law tells us that these forces always come in pairs, and that they are always
equal in magnitude (size) and opposite in direction. If you have ever been driving
and had the unfortunate experience of having a bug hit your windshield, you
have observed action and reaction forces at work.
When a bug strikes the windshield of a moving car, which is greater - the force of
the car pushing on the bug, or the force of the bug pushing on the car? Physics
tells us that these forces are equal. So why does the bug get squashed? The
mass of the bug is so much less than the mass of the car, so the bug
experiences a much greater acceleration. In mathematical terms:
F bug = ma = ma = F car
Friction
Friction is a force which resists an object's motion. It occurs when two surfaces
rub against each other. Two smooth surfaces (like leather soled shoes on ice)
will have very little friction, whereas two rough surfaces (like two pieces of
sandpaper) will have a very large force of friction. The force of Friction (Ff)
always acts in the direction opposite to the object's motion. Friction can prevent
an object from moving (static friction) as when a block of wood rests on an
inclined board. Friction can also change an object's acceleration (kinetic friction)
such as when the brakes are applied on a moving car.
The frictional force acting on an object is given by the equation:
Ff = μ FNormal
where Ff is the frictional force, μ is the coefficient of friction, and FNormal is the
normal force. With this equation we can solve for the static or kinetic friction.
The static frictional force means that the object is at rest, and kinetic frictional
force means the object is in motion.
The coefficient μ is the ratio of friction between the two objects in contact, such
as wood on wood, wood on steel, or rubber on asphalt, and the normal force
present (which depends on the object’s weight).
μ = Ff / FNormal
This is a number without units and it is always less than 1 (wood on wood =
0.3). Coefficients of friction can be found in reference tables. Some examples are
shown here:
Surfaces
Oak on Oak
Steel on Steel
Rubber on Asphalt
Rubber on Ice
μ
0.3
0.4
1.07
0.005
The normal force can be determined if the mass of the object is known. Recall
that when an object is moving along a horizontal plane that the normal force is
equal to the Weight. In fact, they are equal in magnitude and opposite in
direction. Thus both are calculated using mass x acceleration.
FNormal = Fg = mg
PhET Simulation - Friction
PhET Simulation - Ramp With Friction
Examples
1. Determine the kinetic frictional force for a 5kg wood block moving
horizontally on a tile floor if the coefficient of friction between them is 0.35.
Ff = μ FNormal = (μ k)(m)(g) = (0.35)(5kg)(9.8m/s2) = 17.2 N
2. Determine the coefficient of kinetic friction if a 15 N force is required to
move a 2 kg wood block across a horizontal floor.
Ff = μ k FNormal or (μ k) = Ff / FNormal
15 N / (2kg)(9.8m/s2) = 0.765
mk = 0.765
3. If it takes 200N directed west to accelerate a 40 kg file cabinet at a rate of
4m/s2, What is the frictional force?
First determine the force required for this acceleration:
F = ma = (40 kg)(4 m/s2) = 160N
The net force is 160Newtons. If 200 Newtons is applied to push the file
cabinet forward, there must be a frictional force opposing its motion. Thus
40N was used to overcome friction.
200N - 160N = 40N
Ff = 40 N [Backward]