Transcript F n

Kinematics – the study of how things move
Dynamics – the study of why things move
Forces (the push or pull on an object) cause things to move
Aristotle believed that
anything that moves must
have forces being applied
Galileo argued that objects
can move at constant
speeds without forces being
applied . Forces are what
cause objects to accelerate.
Isaac Newton picked up
where Galileo left off.
Lived during the bubonic
plague in England. During
that time, he:
•Invented calculus
•Proposed a law to describe
gravity
•Proposed a theory to explain
color
•Proposed Three Laws of
Motion.
English Physicist,
Astronomer, Theologian
1643 - 1727
Mass
•A measurement of an object’s quantity of matter
•A measurement of an object’s inertia
Inertia – the tendency
of objects to maintain
their state of rest or to
maintain constant
velocity
Example: car slams
on brakes and items
on seat fall to floor
Objects with a larger mass have a greater
inertia. Therefore, they are harder to accelerate
(speed up or slow down)
Inertia can give the impression that forces are
being applied.
Force is not being applied to rider. Rider is
moving at constant velocity because of inertia.
Newton’s First Law – an object at rest tends to
stay at rest and an object in uniform motion tends
to stay in uniform motion (constant velocity)
unless acted upon by a net external force
Newton’s First Law is also
known as the Law of Inertia.
Net force (ΣF) – the sum of all forces that act on
an object.
A free body diagram (FBD) shows all of the
forces that are present on an object both in the
horizontal and vertical direction.
In a FBD, angled forces are resolved into
horizontal and vertical components
Four Basic Forces
Applied force (Fa) – a force that is done by an external
cause (agent). It can be any direction.
Gravitational force (Fg or W) -- the force caused by
gravity (weight). It always acts
downward.
Frictional force (Ff) -- a force that opposes motion and
slows down objects. It is always parallel
to the surface.
Normal force (Fn) – the force exerted by a surface on
which an object is resting. It is always
perpendicular to the surface.
Example: book being pushed on table
book
FBD
Net Force
Equations
Fn
Fa
Ff
book
Fg
Σ Fx = Fa - Ff
Σ Fy = Fn - Fg
Forces at Angles
Fay = Fasin40
Fa
40°
book
Fax = Facos40
FBD
Net Force
Equations
Fay
Fn
Fax
book
Ff
Fg
Σ Fx = Fax - Ff
Σ Fy = Fn + Fay - Fg
Newton observed some things about
accelerating objects:
•The bigger the force, the greater the acceleration
•The larger the mass, the smaller the acceleration
Newton’s Second Law – the acceleration of an
object is directly proportional to the net force
acting on the object and inversely proportional to
its mass
Σ F = ma
F = force (Newtons)
m = mass (kg)
a = acceleration (m/s2)
What net force is required to bring a 1500-kg
car to rest from a speed of 28 m/s within a
distance of 55 m?
A 70-kg person traveling at 100 km/hr strikes a
parked car. At the instant of impact, the seat belt
restrains the person with a force of 21,000 N bring
them to rest in the car. How far does the person
travel before coming to rest?
When a force is applied to an object, it is always exerted
by another object.
Examples: a hammer hits a nail
a child pulls a sled
an apple is pulled to the Earth
Newton believed that the “force-providers” also are
“force-receptors.”
Examples: the nail pushes back on the hammer
the sled pulls back on the child
the Earth is pulled to the apple
Newton’s Third Law – Whenever one object exerts a
force on an second object, the second exerts an equal
force in the opposite direction on the first
If every force has an equal and opposite force, why dos
objects ever move?
The forces are NOT exerted on the same object.
Example: If a
hammer exerts a
50-N force on a
nail, the nail
exerts a 50-N
force on the
hammer in the
other direction.
Evidence:
Hammer causes
the nail to
accelerate (+ force)
while the nail
causes the
hammer to
decelerate (- force)
Weight
• A measure of the
gravitational force
on an object
• Always directed
downward (toward
the center of the
Earth
Fg = mg
A person’s mass does not change, but his weight
does depending on the magnitude of gravitation
force.
An average man has a weight of 686 N on the
Earth. What would his weight be if he was
standing on the moon (ag = 1.6 m/s2)
A person pulls upward on string attached to a
box with a force of 150 N. The box has a mass
of 12 kg. Does the box move upward and if
so, with what acceleration does it move?
Normal Force
• A contact force
that is
perpendicular to
the surface
• The force that
pushes up on the
object resting on
the surface
Since the statue is at rest FN is equal and
opposite to FG. FN has another equal and
opposite force (F’N is reaction force on table)
A 65-kg woman descends in
an elevator that briefly
accelerates at 0.20g
downward. She stands on a
scale that reads in N. What
is her weight and what does
the scale read? What does
the scale read when the
elevator descends at a
constant speed of 2.0 m/s?
Should the scale read
the same, more or less
than her weight?
Resultant Force and Equilibrium
Multiples forces on an object must be broken
down into x and y components to find the
resultant force.
What is the resultant
force (magnitude and
direction) acting on the
boat by workers A and
B?
An object is stationary
when all forces acting
on it cancel out. This
situation is called
equilibrium.
What are the
tensions in FA and
FB?
Pulleys
Pulleys utilize ropes or
cables which have a
constant tension force
throughout their length
If multiple lengths of rope
extend from the mass being
lifted, the tension force pulls
up for each extension.
A mover is trying to lift a piano up
to a second story apartment. If
the piano is 2000 kg, what force
does he need to apply to lift the
piano at a constant speed?
If he fatigues and only can lift
with 500 N of force, what will be
the acceleration of the piano?
Friction
Friction is the resistance that an object experiences when
moving.
Caused by a rough surface.
Object on a rough surface
actually has to move up and
down because the two rough
surfaces catch on each other.
Because energy is used to
move the moving object up and
down, less energy is used to
move the moving object
forward.
The force of friction is
influenced by two
factors – the surface on
which an object is
moving and the weight
(gravitational force) of
the object.
Ff = μFn
Coefficient of friction (μ) – indicates
the “roughness” of the surface.
Unique to each surface.
Typically, the normal force of the
object is just equal and opposite to
the gravitational force (but not
always).
Two Types of Friction
Static (Stationary Object)
If an object is at rest, an applied force has to exceed the
maximum static frictional force of the object for it to move
static
friction
applied
box at
rest
Ffs = μsFn
Kinetic (Moving Object)
If an object is moving, there is a kinetic frictional force
that opposes motion (always less than static frictional
force)
applied
box in
motion
kinetic
friction
Ffk = μkFn
When an object
is at rest, friction
is equal to the
force applied to
an object until
the maximum
static force is
attained.
Beyond that
maximum force,
the object moves
and friction
reduces to the
constant kinetic
friction force.
A 10.0-kg box rests on a horizontal floor. The coefficient of static
friction is 0.40 and the coefficient of kinetic friction is 0.30.
Determine the maximum static frictional force and the kinetic
frictional force. Would the box move if a 10 N force was applied? If
so, what would be its acceleration?
Would the box move if a 40 N force was applied? If so, what would be its
acceleration?
Inclined Planes
Inclined planes are unique because gravity is the
accelerating force, but the motion is not vertical (not
free-fall).
Normal
Friction
Gravity
Normal
Friction
Gravity
To solve, rotate the object so the
majority of forces are in x and y
directions (gravity is not).
Normal
(Fn)
y
x
Friction
(Ff)
Resolve gravity into the new x
and y components.
Fgy
Gravity
(Fg)
Fg
Fgx
Write net force equations
Σ Fx = Fgx - Ff = ma
Σ Fy = Fn - Fgy = 0
A skier with a mass of 85 kg begins to descend a 30
degree slope. Assuming the coefficient of kinetic friction
is 0.10, calculate his acceleration.