Prof.
Clements Notes/Hints for Physics Courses
Chapter
4 Part 2 Open Stax College Physics or Most Introductory Physics
Courses
Newton's
Third Law; Normal Force, Tension
Terms
you should know at the end of this unit: free body diagram, tension,
normal force, inertial reference frames
Newton’s
Third Law of Motion
Can
you think of a force in the universe that does not have another force
associated with it that is equal in magnitude but opposite in
direction? The correct answer is, “NO.”
There
are no isolated (unpaired) forces in the universe.
Newton's Third Law:
Whenever one object exerts a force on a second object, the second
object exerts an equal and oppositely directed force on the first
object. F21 = - F12
Examples:
1. As you stand
stationary on the floor:
a) There is a
downward force on the floor due to your weight.
b) There is an
upward force of the floor acting on your feet.
These two forces
have the same magnitude (measured in Newtons, or pounds), but the
forces act on different objects (floor, you) and are in opposite
directions. Your weight pushes down. The floor pushes up.
2. As you walk
North across a floor:
a) There is a
horizontal force on the floor as you foot pushes on the floor.
b) There is a
horizontal force on your foot as the floor pushes on your foot.
These two forces
have the same magnitude (measured in Newtons, or pounds), but the
forces act on different objects (floor, foot) and are in opposite
directions. Your foot pushes in the South direction on the floor.
The floor pushes in the North direction on your foot. (Notes: The
forces of example 1 are still active in the vertical direction. The
force of friction allows walking to take place. Friction will be
discussed later.)
3. For the case of
a baseball being hit by a bat:
a) There is a
force on the ball towards the outfield due to the bat.
b) There is a
force on the bat towards home plate due to the ball.
These two forces
have the same magnitude (measured in Newtons, or pounds), but the
forces act on different objects (ball, bat) and are in opposite
directions. The bat pushes the ball towards the outfield. The ball
tries to push the bat towards home plate.
The name “Action
Reaction” for Newton’s Third Law is misleading in that there is
no time delay for the appearance of the “reaction” force. The
two forces have equal magnitudes at all times.
The “action
reaction” forces always act on different objects.
Make
a force diagram for a student who is sitting in a chair. Draw all of
the forces that act on the student and all of the Third Law paired
forces. You should have an upward force arrow on the person due to
the force of contact with the chair. You should have a downward
force arrow on the person due to the gravitational force on the
person by to the Earth. You should have a downward force arrow on
the chair due to the weight of the person. You should have an upward
force arrow at the center of the Earth due to the gravitational
attraction on the Earth by the person.
It
is very important to note that only the forces acting on the object
of interest are used in the calculations. You will not use all of
the forces drawn in your first sketch.
Systems
of Objects and Free-Body Diagram
In systems where
there is more than one object you should start your analysis by
finding the net EXTERNAL force acting on the system and the total
mass of the system. Then you will be able to calculate the
acceleration of the system. After this step you will draw the force
diagram for a section of the system and calculate the tension in the
connection between the masses.
When a force
diagram only shows the forces acting on the object of interest it is
called a free-body diagram.
Example:
A massless rope is attached to a block of wood that has a mass of 8
kg. A student is pulling to the right on the horizontal rope with a
force of 9 Newtons. A 3 kg block of aluminum is attached by a
massless string to the left side of the block of wood. The wood and
aluminum are on a horizontal table. Ignore friction. Calculate the
force the string applies to the aluminum object.
Start:
Find the acceleration of the system. Only use external forces.
There is only one external force, the 9 Newton force acting to the
right. Use F = ma The total mass of the system is 11 kg.
9
Newtons = 11 kg * a
a
= 0.818 m/s2
Next:
Find the tension in the string connecting the aluminum and wood
objects. The object of interest is now the aluminum object. The
only external force acting on just the aluminum object is the tension
in the string. The 9 Newton force does not act directly on the
aluminum object so it is not considered.
Use
F = ma
The
force is the tension in the string. The mass for the object of
interest is 3 kg. The acceleration values for the aluminum and wood
are both 0.818 m/s2 .
Tension
in string = 3 kg ( 0.818 m/s2 )
Tension
in string = 2.45 Newtons
The
apparent weight (measured by a bathroom scale) of a person riding in
an elevator which is accelerating upward at 1 m/s2 is
larger than the weight of the same person standing in the elevator as
it moves upward at a constant rate of 3 m/s.
Use
F = ma
The
net force is the addition of the upward force of the bathroom scale
on the person and the downward weight of the person.
Forcescale
– mg = ma
Forcescale
= mg + ma mg is the weight of the person. Forcescale
is larger than mg.
Note:
When the elevator reaches a constant speed the acceleration = 0 and
Forcescale = mg.
Note:
When the elevator nears the top of its motion the acceleration
becomes negative and
Forcescale = mg + m(-a) and Forcescale <
mg .
In
September 2017 this YouTube video was available to show this effect.
You
might want to search YouTube for other videos about scales and
elevators. It is a popular topic for physics classes.
Normal,
Tension, and Other Examples of Forces
Contact force: a
force that occurs between two objects when they are touching
There are always
pairs of forces in contact force situations but only the force acting
on the object of interest is useful for the calculations.
Normal
force: a contact force that is perpendicular to the surface
Tension
in a rope is a force.
Inclined Plane
Problems
When an object is
on an inclined plane the weight vector is not parallel to the plane
and is not perpendicular to the plane. Remember that when we write
equations we must only use quantities that are parallel to each
other. We will be interested in the velocity along the plane and the
displacement along the plane. The components of the weight vector
can be used in the equations.
Suppose a 7 kg
object is resting on a frictionless inclined plane that has an angle
of 34 degrees. The object is 1.4 meters up from the bottom of the
plane. It is released from rest at a certain instant of time. Draw
a free-body diagram at this time with the goal that you will
calculate the time for the object to reach the bottom of the plane.
Steps to be done:
1. Calculate the
component of the weight acting down the plane. Calculate the
component of weight perpendicular to the plane.
2. Calculate the
acceleration of the object down the plane using F = ma.
3. Calculate the
time required for the object to reach the bottom of the plane using a
kinematic equation.
The force of
gravity perpendicular to the plane is not important in the
calculation because it is not parallel to the plane. When friction
is present this force will be used to determine the force due to
friction.
A person is
standing for 10 minutes, stationary, on a tight rope that is tied
between two poles. It impossible for a real rope to not sag when a
person is standing on the rope. The net force on the person in the
vertical direction must be zero for the person to be stationary. As
the rope sags the tension of the rope now has an upward component
that balances the downward weight of the person.
An inertial
reference frame is a frame in which Newton's Laws are valid. An
inertial reference frame may be moving, but it is not accelerating.
If the observer is in a non-inertial reference frame the observer
will think there are forces present that don't actually exist.
Copyright©
2017 by Greg Clements Permission is granted to reproduce this
document as long as 1) this copyright notice is included, 2) no
charge of any kind is made, and, 3) the use is for an educational
purpose. Editing of the document to suit your own class style and
purposes is allowed.
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