Download Forces notes from class 16-17

Force
What is a force?
-A force is a “push” or “pull” that is applied to an object.
Where are forces located?
-A force occurs at a point of contact between the object and some
identifiable agent that exerts the force.
-A force can be exerted by an animate or inanimate agent.
Give an example of a force you have experienced continuously all
your life.
The force of gravity (this is also called “weight”).
*Gravity is the only long-range force (a.k.a. non-contact force) that
we will study in this class.
Gravity is most accurately described by
the general theory of relativity (proposed
by Albert Einstein in 1915) which describes
gravity not as a force but as a consequence of the
curvature of spacetime caused by the uneven
distribution of mass/energy; and resulting in
gravitational time dilation, where time lapses
more slowly in a lower (stronger) gravitational
potential.
"Gravity." Wikipedia. Wikimedia Foundation, n.d. Web. 30 Sept. 2016.
Force
Give an example of a situation where an object is given a force but is
not moved.
Pushing on a car when it is in park.
Pushing on a lab table that is bolted to the floor.
You have a force of weight (gravity) acting on you right now, but you
are not moving!
What object do we use to measure force?
A spring scale.
Identifying Forces
1. Divide the problem into the system and the environment
System : the object whose motion you wish to study
Environment : everything else
2. Draw a picture of the problem, showing the object and everything
in the environment that touches the object.
3. Draw a closed curve around the system, with the object inside the
curve and everything else outside the curve.
4. Locate every point on the boundary of this curve where the
environment touches or contacts the system. Do not leave any out!
5. Identify by name the contact force or forces at each point of contact,
then give each an appropriate symbol.
6. Identify any long-range forces. For now, the only one is gravity.
Types of Forces
FW = Weight Force
caused by gravity
direction is always down (e.g. towards earth)
the only long-range force we will use
FN = Normal Force
caused by contact with a surface
direction is perpendicular to the surface
Ff = Friction Force
caused by (attempted) sliding between surfaces
direction opposes (desired) motion
FT = Tension Force
caused by a pulling rope, string, chain, etc.
FD = Drag Force
caused by air resistance (or water, etc.)
direction opposes motion
FA = Applied Force
any other applied force (e.g. from a motor)
Free Body Diagrams
A FBD is a drawing of all the forces acting on the object.
FBD’s are the Physics of forces. Everything else is just math.
How to Draw a FBD
1. Make a list of all forces acting ON the object
2. Draw them in the correct orientation within a coordinate system
Common Mistakes with FBD’s
-Identifying a force correctly, but not knowing which way it points
-Including forces exerted by the object
-Using no coordinate system, or an inappropriate one
-Placing the tips of vectors at the origin, rather than the tails
-Making errors when determining the components of force vectors
-Placing action-reaction force vectors on the wrong diagrams
Newton’s First Law of Motion
Explain Aristotle’s (wrong) idea about force.
Aristotle thought that a force was required to keep an object moving.
He thought: if no force acts on an object, it cannot move.
What effect confused Aristotle into having this view?
The fact that a force called “friction” acts on objects, causing them to
slow down and stop. Without friction, objects with no force on them
could still move.
Newton’s First Law of Motion
State Newton’s First Law.
“An object at rest tends to stay at rest, and an object in motion tends to
stay in motion unless acted on by an outside force.”
If all of the forces on an
object balance out
If there is no net force
on an object
If the sum of all of the
forces on an object is
zero
constant velocity.
then the object
moves with
constant speed in a
straight line path.
Newton’s First Law of Motion
What does the term “net force” mean?
“Net force” is the resultant force on an object when all force vectors
(on the object) are added. It is the vector sum of all forces acting on an
object.
Quick question: what is the net force on you right now?
Does this mean that there are no forces acting on you at all?
Newton’s First Law of Motion
What is inertia?
Inertia is how much an object resists changes in motion.
It is both “how hard it is to get an object to speed up” and “how hard
it is to get an object to slow down.”
Newton’s First Law is sometimes called the “Law of Inertia”
Mass
Give TWO definitions of “mass”.
How much matter an object is made of.
How much inertia the object has.
What units do we use to measure mass?
Kilograms
We use a “balance” to measure mass, not a scale!
Newton’s Second Law of Motion
Write Newton’s Second Law as an equation and explain what the S
symbol means.
Operational Form:
Elegant Form:
 F  ma
or
Fnet  ma
The symbol S is “sigma” and means “the sum of”.
Newton’s Second Law of Motion
What type of motion does an object with a net force have?
If the net force is constant, then the object has a constant acceleration.
Write Newton’s Second Law as a sentence.
Force equals mass times acceleration.
The net force on an
object
equals the object’s mass times the
object’s acceleration.
The sum of all of the
forces on an object
Example 1: Elevator
An elevator is going up at a steady speed.
What forces are acting on the elevator?
-Tension and Weight
Is the magnitude of FT greater than or less than the magnitude of FW?
They are equal because there is no acceleration.
Remember: motion does not require a net force.
Motion requires no cause. Only change in motion requires a cause.
Example 2: Block Pushed
A block is pushed across a table at a steady speed.
A force is being exerted on the block. Why isn’t it accelerating?
-Identify all forces and draw a FBD of the block
-Compare the size of the pushing force and the friction force
-Acceleration results from NET force, not individual forces
Example 3: Block Sliding
A block is pushed across a table at a steady speed.
What forces are acting on the block while it slides?
-The NET force is the friction force
What is the direction of the net force?
What is the direction of the acceleration?
Example 4: Ball Tossed Straight Up
How does the ball move upward without an upward force?
Remember: motion requires no cause.
Inertia continues the current motion.
This question is the wrong question. What is the right question?
Why does the ball slow down and eventually fall?
This is similar to the horizontally sliding block:
Why does the block slow down and eventually stop?
Newton’s Second Law of Motion
Consider several objects. A single force acts on each object. Sketch a
graph of each of the following:
All the objects have the same mass, but are given varying
accelerations. Sketch the force acting on the objects as a function of
acceleration.
F
a
Section 4-4: Newton’s Second Law of Motion
Consider several objects. A single force acts on each object. Sketch a
graph of each of the following:
All the objects have the same acceleration, but have different masses.
Sketch the force acting on the objects as their mass varies.
F
m
Section 4-4: Newton’s Second Law of Motion
Consider several objects. A single force acts on each object. Sketch a
graph of each of the following:
All the objects have the same force acting on them, but have different
masses. Sketch their acceleration on the various masses.
a
m
Section 4-5: Newton’s Third Law of Motion
State Newton’s Third Law of Motion
“For every action, there is an equal and opposite reaction.”
If object A exerts a force on object B, then object B exerts a force on
object A that is equal in magnitude, but opposite in direction.
These two forces (object A pushes object B, object B pushes object A)
are called an “action/reaction pair” of forces.
What is very important to remember about the “action” and “reaction”
forces of an action/reaction pair?
The two forces of an action/reaction pair act on different objects!
Section 4-5: Newton’s Third Law of Motion
When you stand, the floor exerts an upward force on your feet. What
is the reaction force?
Your feet push down on the floor.
The Earth exerts a downward gravitational force on you. What is the
reaction force?
You pull (by gravity) upward on the Earth.
Section 4-5: Newton’s Third Law of Motion
Name the action and reaction forces that occur when you walk.
Your feet push backward on the floor.
The floor pushes forward on your feet.
The force responsible for this is the friction force.
Feet on
floor
Floor
on feet
Section 4-6: Weight—The Force of Gravity; and Normal Force
What symbol do we give to the force of weight?
Either FW, Fg, or W
What is the equation for the force of weight on an object?
Fw = mg
What is the direction of the force of weight on any object?
Down!
Section 4-6: Weight—The Force of Gravity; and Normal Force
What is a contact force?
A force that can only be applied when one object touches another
object.
What is “normal force”?
The force that a surface (floor, tabletop, wall) exerts on an object that
is touching the surface.
The normal force’s job is to prevent the object from “breaking
through” the surface.
The symbol for normal force is FN (sometimes just N).
Section 4-6: Weight—The Force of Gravity; and Normal Force
What is the equation for normal force?
Kidding! There is no equation for normal force.
In order to find normal force, we must use Newton’s Laws to analyze
the situation, create an equation relating the forces acting, and solve
for normal force.
What is the direction of the normal force on any object?
Perpendicular to the plane of the surface. “Normal” is a math word
that means “a line (the force) is perpendicular to a plane (the surface)”.
Section 4-6: Weight—The Force of Gravity; and Normal Force
When you stand still on the floor, your weight force of gravity is equal
and opposite to the normal force the floor exerts on you. Explain
whether this is an action/reaction pair.
It is NOT!
Both forces act on the same object (you). Action/reaction pairs sound
like this: “A pushes B, so B pushes A”. Action/reaction forces act on
different objects!
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
What is a free-body diagram?
A diagram that shows all of the forces (depicted as vectors) acting on a
single object.
What is the tension force?
The force that a rope, string, or cable exerts.
The symbol for the tension force is FT (sometimes just T).
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
What is the equation for tension force?
Kidding! There is no equation for tension force.
Like normal force, we must use Newton’s Laws to determine the
tension force acting on any object.
What is the direction of the tension force on an object?
The direction that the rope/string “points” away from the object.
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is at rest.
FN
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is at rest.
FT
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is at rest.
FT2
FT1
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Constant velocity, no friction.
FN
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
No friction.
FN
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Friction prevents sliding.
FN
Ff
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is at rest.
FN
FT
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is at rest.
FN1
FN2
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock accelerates upward at 9.8 m/s2.
FT
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is in free-fall. No air resistance.
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock falls with constant velocity through the air.
Fair
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is in projectile motion.
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock is at the peak of projectile motion.
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Friction causes the rock to come to rest.
FN
Ff
No more forces!
Fw
Section 4-7: Solving Problems with Newton’s Laws: Vector Forces
and Free-Body Diagrams
Draw a free-body diagram on each object. Draw longer arrows for
stronger forces.
Rock accelerates to the right at 2g.
FT
No more forces!
Fw
Section 4-8: Applications Involving Friction, Inclines
What is “kinetic friction”?
The frictional force that is applied to an object when it is SLIDING
along (or against) a surface.
What is the friction force proportional to?
The weight of an object!
The normal force acting on the object from the surface.
Section 4-8: Applications Involving Friction, Inclines
What symbol do we give to the force of friction?
Ff (sometimes just f)
What is the equation for kinetic friction?
Ff = µkFN
What does the symbol k stand for?
The coefficient of kinetic friction.
Coefficients of friction have no units.
Section 4-8: Applications Involving Friction, Inclines
What does the k depend on?
On what the object and the surface are made of.
Section 4-8: Applications Involving Friction, Inclines
What is static friction?
The force of friction that tries to prevent an object from beginning to
slide along a surface.
What is the equation for static friction?
Ff  µsFN
What does the symbol s stand for?
The coefficient of static friction.
Section 4-8: Applications Involving Friction, Inclines
Why is there a  sign in that equation?
Static friction has a maximum force that it can apply before the static
friction “breaks” and the object begins to move.
Example: A 5 kg block rests on a surface where the coefficient of
static friction is µs = 0.4.
What is the object’s weight? 50 N
What is the normal force on the object?
Also 50 N
If a 10 N force acts horizontally on the block, will it move?
No—the maximum amount of static friction is µsFN = (0.4)(50) = 20 N
Is the amount of friction acting on the block 20 N?
No—friction is only 10 N to counteract the applied 10 N.