Transcript Lecture 02 - WebPhysics

Goal: To learn about Forces
Objectives:
1) To explore the basics of force and Newton’s
first law
2) To learn about weight and compare to mass
3) To learn about the Normal force
4) To learn about frictional force
5) To learn about Tension
6) To learn about force vectors and net force
Newton’s First Law
• An object in rest or in motion will stay in
rest or in motion until acted upon by an
outside force
• This is called the law of inertia
• In other words, to change an objects
motion (and you can consider at rest a
“motion”) you have to do something to it
Force
• There are many different forces in the
universe.
• The main 4 are:
– A) Gravity
– B) Electromagnetic
– C) Strong
– D) Weak
Force is a VECTOR
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Force is a vector
Force has DIRECTION!
Force ALWAYS has direction
So, the units of force are Newton direction
Newton is N
So, a force could be +3 N up, +2 N down,
-12.3 N forward, +72.8 N north, ect
Something we will look at in this
class:
• Gravity near the surface of the Earth.
• Near the surface of the Earth the force of
gravity is fairly straightforward
• Gravity force = mg
• If there are no other vertical forces (other
than a Normal force) then the gravity force
is the Weight
• Note that Weight is a FORCE
Questions
• 1) What is the unit(s) of Weight?
• 2) g = 9.8 m/s2 does it have a direction?
Weight vs Mass
• On the Earth I have a mass of about 90 kg
and a weight of about 205 lbs (880
Newtons).
• On the moon gravity is 1/6th what it is on
the earth.
• What is my mass and weight on the
moon?
Normal Force
• Anytime you contact something there is a
Normal Force (Newton’s 3rd law, equal and
opposite force)
• The normal force is the force that pushes
you away from a surface and is
perpendicular to the plane of that surface.
• What would happen if you stood on a
surface that had no normal force?
How to find the normal force
• Find the sum of all the non normal forces.
• If the object is not moving in the vertical direction
(that means there is no total force – which we
call a net force) then the normal force is the
force needed to cancel out all the other forces.
• So, if there is just gravity, then the normal force
is equal to the weight.
• If I pull up on something then the normal is less
because the total downward force (and up force
is effectively a negative down) is less.
• If I push down then the normal force increases.
Friction
• One force you are probably familiar with is
friction.
• Friction is always a force that opposes
motion – that is the direction is opposite
the direction of motion.
• There are actually two type of frictional
forces.
• The first is called Static Friction
Static Friction
• Static Friction is caused because on a
microscopic level nothing is perfectly
smooth.
• The bumps and pits of the two objects
touching makes things rub and rip off
small pieces.
• This takes energy to do which causes the
static friction.
Kinetic Friction
• Once an object starts to slide across
another object it now glides over the top of
the bumps and pits.
• As a result the force of friction is cut in
half.
• A tire is stationary on the ground normally.
If a tire slides you loose friction and you
loose control.
Friction Equation
• F=μN
• I am 90 kg. I walk down a sidewalk which has a
frictional coefficient of 0.2
• A) Find my normal force
• B) What is the frictional force on me
• C) What force do my legs need to exert to keep
myself walking at a constant velocity and how do
you use Newton’s First Law to determine this?
Tension
• Forces provided by strings or wires are called Tensions.
• The Tension in a wire is similar to the normal force
except that it pulls an object towards it instead of
pushing away.
• To find tension either:
• A) compare the total force to all the forces exerted on the
string. The difference will be the tension of the string.
• B) find the force the string is exerting on something else
Tension example
• A 10 kg mass is tied to the end of a string
and allowed to hang.
• A person pulls down on the string with a
force of 150 N.
• A) What is the tension of the string if the
mass does not move (Hint, Newton’s first
law)?
Force Vectors
• In reality forces will often times have
components in more than 1 dimension.
• This creates a vector.
• In order to solve for problems where you have
forces in more than 1 dimension you need to
create 2 accounts, that is 2 problems that are
separate from one another.
• This is similar to having a checking account and
a savings account.
Calculator note
• Everyone use their calculators to find the
answer to the following problem (even if
you can do this one in your head):
• (2 * 6) / (3 * 4)
Vector Break down
• Since the 2 components will be 90
degrees from each other you can use the
following to find each component.
• Lets call the total force Ft
• The opposite leg in our right triangle has a
length of: Ft sin(theta) where theta is the
angle
• Adjacent is: Ft cos(theta)
• Finally tan(theta) = Opposite / Adjacent
One way to remember which is
which
• Sin(0 degrees) = 0
• So, ask yourself would this value be 0 if
the angle is 0? If the answer is yes then
use sine
• Cos(0 degrees) = 1
• Ask yourself, if the angle was 0 would the
total force be just this force? If the answer
is yes then use the cosine.
Adding Force vectors
• Once you break a force into its components (for
this class we will often use x and y) now you are
ready to add them.
• The x’s add to the x’s because the x direction is
a UNIT!
• Same for the y’s because the y’s are a UNIT
• If you need a magnitude at the end, which you
may for the homework then once you have the
total x and total y you can use the Pythagorean
Theorem.
• However, as we get further along we will treat
the x and y as separate problems and may have
to solve for 1 to get the other.
Net Force
• Once you add up all the vectors for all the forces
you have what is called the Net Force
• The Net Force will determine how the objects
motion is changed
• Note that the Net Force is a vector.
• It can have x and y components – and if any are
non-zero, then its motion in that direction will
change.
• Meanwhile in any direction that the net force is
exactly zero the motion in that direction will be
constant (even if the motion is zero).
Net Force
• Net Force = sum of all forces
• Net Force = mass * net acceleration
• For example, if you have vertical forces, and
need to solve the net force, find the net force
from mass * net acceleration
• Then, plug that answer into Net Force = sum of
all forces so that you can solve for the Normal
force
Your turn!
• The 3 Stooges decide to open a moving company and someone is
crazy enough to hire them.
• The 3 are moving a rather large box by pushing it across the floor.
• Luckily the floor is slippery due to all the banana peals that…. Well
that is another show. Anyhow, no friction
• Larry pushes on the box from behind. He pushes at an angle 30
degrees below the vertical with a force of 200 N.
• Curly (who has a mass of 70 kg) sits on the box. Not much help
there…
• Mo pulls on the box at a 45 degree angle with a force of 350 N.
• The box has a mass of 50 kg.
• A) What is the net force on the box in the vertical direction (call this
the y direction)? Hint, will the box lift off the ground?
• B) What is the normal force on the box (and no it is not = mg)?
• C) What is the net force on the box?
Conclusion
• We have learned about force.
• We have learned how to compute gravitational
force
• We have learned how to find a normal force.
• We have learned how to use that normal force to
find the frictional force
• We have learned how to find tension
• We have learned how to turn Forces into vectors
and add those vectors to create a net force.