- [Instructor] What's Newton's first law say?
Newton's first law states that objects don't change
their velocity unless there's an unbalanced force.
So, if there was no force on an object,
or the forces are balanced, then the object
will continue moving with a constant velocity.
Or, if it was at rest,
it'll continue sitting at rest.
In other words, there doesn't have
to be a net force for something to have motion,
there only has to be a net force
for something to have acceleration.
And it's really important to note
that Newton's first law does not apply to single objects.
It applies to systems of objects as well.
In other words, if you consider a system of objects,
and look at the center of mass of that system,
the center of mass of the system
will remain at rest or remain in constant motion
as long as there's no external
unbalanced forces on the system.
So these objects may be exerting forces on each other,
but the center of mass will remain at rest,
or with constant velocity unless
there's an unbalanced external force
on this system of particles.
So what's an example problem involving
Newton's first law look like?
Say you were told that a heavy elevator
is lifted upward by a cable exerting a force Fc,
and the elevator moves up with a constant velocity
of five meters per second.
We wanna know how the force from the cable
compares to the force of gravity.
The mistake many people make is they think
that since the object was moving upward,
the upward force must be larger,
but that's not true.
Since this is moving upward with constant velocity,
the forces actually have to balance.
Since Newton's first law states
that when the net force is zero,
the object maintains a constant velocity.
And for the net force to be zero,
these forces have to cancel.
So, even though it's non-intuitive,
this cable force has to equal the force of gravity,
so that the elevator can move with constant velocity.
What's Newton's second law mean?
Newton's second law states that
the acceleration of an object is proportional
to the net force and inversely proportional to the mass.
Which, written in equation form,
states that the acceleration of an object
is equal to the net force on that object
divided by the mass of the object.
And this equation works for any single direction as well.
In other words, the acceleration in the x direction
is equal to the net force
in the x direction divided by the mass.
And the acceleration in the y direction
is equal to the net force
in the y direction divided by the mass.
So what's an example of Newton's second law look like?
Let's say a five kg space rock
had the forces acting on it shown in this diagram,
and we wanted to determine the acceleration
in the horizontal direction.
Since horizontal is the x direction,
we're only gonna use forces in the x direction
to determine the acceleration in the x direction.
That means the 15 Newton force,
and the five Newton force don't contribute at all
to the acceleration in the x direction.
The only components that contribute
are the horizontal component of the 10 Newton force,
which would be 10 cosine of 30,
and the 40 Newton force.
So the acceleration in the x direction
would equal the net force in the x direction,
which would be 10 cosine 30.
That would be a positive contribution,
since it points to the right,
minus 40, since that's a negative
contribution pointing to the left.
And finally we'd divide by five kilograms,
which gives us the correct acceleration in the x direction.
What's Newton's third law mean?
Newton's third law states that if an object A
is exerting a force on object B,
then object B must be exerting an equal
and opposite force back on object A.
And this is true even if the objects
have different sizes or there's acceleration.
In other words, let's say the Earth
is pulling on an asteroid.
Even though the Earth is much larger than the asteroid,
the asteroid's gonna exert an
equal and opposite force back on the Earth.
And this is true whether the asteroid
is moving with constant velocity,
or whether it's accelerating.
So what's an example problem
involving Newton's third law look like?
Let's say a metal sphere is sitting on a cardboard box,
and we want to determine which of these choices
constitute a Newton's third law force pair.
The first option says that there's
an upward force on the sphere from the box.
So to find the third law pair,
just reverse the order of the objects,
which means the partner to this force
would be the force on the box by the sphere,
which is not what this says, so it's not option A.
Option B refers to an upward force
on the box from the table,
which we know if we reverse the labels,
should have a partner force that would be the force
on the table by the box.
Which is not what this says, so it's not option B.
Option C talks about an upward force on the sphere
from the box, which, reversing the labels
gives us a partner force of on box by sphere.
Which is not what this says, so it's not option C.
And D refers to an upward force on the box from the table,
which, if we reverse the labels,
gives us a partner force on the table by the box,
which is what this says, and so the forces in D
constitute a Newton's third law force pair.
Which means they must always be equal and opposite.
Other pairs might be equal and opposite,
but no matter what happens,
these two forces have to be equal and opposite.
How do you find the force
of gravity on objects near the Earth?
The force of gravity on all objects near the Earth
is down toward the center of the Earth,
and it's equal to the mass
times the acceleration due to gravity.
Another word for the force of gravity
is the weight of an object.
But be careful, the weight is not the mass.
Weight is the force of gravity which means
weight is m times g not just m.
The force of gravity is a vector,
and it has units of Newtons.
So what's an example problem involving
the force of gravity look like?
Let's say you knew the mass and weight
of a watermelon to be 5 kilograms and 49 Newtons
when you measure them on the Earth.
What might the values for mass and weight
of that watermelon be when it's brought to the moon?
The value of the mass isn't gonna change here
since it's a measure of the total amount
of substance in that object.
But the weight of the watermelon on the moon
is gonna be less since the gravitational pull
is gonna be weaker on the moon.
So the only choice consistent with those two conditions
is A since the mass stays the same and the weight decreases.
What's the normal force?
The normal force is the outward force
exerted by, and perpendicular to a surface.
There's no formula specifically to find the normal force,
you simply have to use Newton's second law.
Let normal force be one of the unknowns,
and then solve for it.
Now, if you've just got a mass
sitting on a horizontal surface,
and there's no extra forces involved,
the normal force is just gonna counter
the force of gravity, which means
the normal force will just be mg.
But if there's extra forces,
or there's acceleration in the direction
of the normal force, then the normal force
is not gonna equal mg,
and you'd have to use Newton's second law
for that direction to solve for it.
The word normal in normal force
refers to the fact that the force
is always perpendicular to the surface
exerting that force.
And it's good to remember that,
for a mass on an incline,
that normal force is not gonna be equal to mg.
It's gonna be mg times cosine of theta.
The normal force is a vector, since it's a force,
and it also has units of Newtons.
So what's an example problem
involving normal force look like?
Let's say a person is pushing
on a stationary box of mass M
against the ceiling with a force Fp,
and they do so at an angle theta.
We want to know what's the magnitude
of the normal force exerted on the box from the ceiling?
So we'll draw a force diagram.
There's the force Fp from the person,
the force mg from gravity.
If the box is stationary there'd have to be a force
preventing it from sliding across the ceiling,
which is most likely static friction.
And there's also gonna be a normal force,
but that normal force will not point upward.
The normal force from the ceiling cannot pull up on the box.
The normal force from the ceiling will only push
out on the box, which will be downward.
Since our normal force is in the vertical direction,
we'll analyze the forces in the vertical direction.
And we can see that the forces must be balanced
vertically, since this box has no motion vertically.
In other words, the normal force
plus the gravitational force is gonna have to equal
the vertical component of the force Fp.
Which, since that's the opposite side from this angle,
we can write as Fp sine of theta.
And now we can solve for the normal force,
which gives us Fp sine theta - mg.
Note that we did not have to use the force of friction,
or the horizontal component since our normal force
was in the vertical direction.
What's the force of tension mean?
The force of tension is any force
exerted by a string, rope, cable, cord
or any other rope like object.
And unlike the normal force
that can only push, tension can only pull.
In other words, ropes can't push on an object.
But, similar to the normal force,
there's no formula for tension.
To find the tension, you'd insert the tension
as an unknown variable into Newton's second law,
and then solve for it.
Since the force of tension is always pulling on objects,
when you draw your force diagram,
make sure you always draw those tension forces
directed away from the object
the string is exerting the tension on.
Tension's a vector, since it's a force,
and it has units of Newtons.
So what's an example problem involving tension look like?
Let's say two ropes are holding up a stationary box,
and we wanna know how the magnitudes
of the tensions in both ropes compare.
Drawing our force diagram there'll be a downward
force of gravity, a force of tension to the left,
and also a diagonal force of tension up and to the right.
Since the box is stationary,
the forces have to be balanced in every direction.
That means the vertical component of T2
has to equal the magnitude of the force of gravity,
and the horizontal component of T2
has to equal the magnitude of the force T1.
But if a component of T2 equals the entire T1,
then the total tension T2 has to be bigger than T1.
In other words, if part of T2 is equal to T1,
then all of T2 is greater than T1.
What's the force of kinetic friction mean?
The force of kinetic friction is the force exerted
between two surfaces that are sliding across each other.
And this force always resists the
sliding motion of those two surfaces.
The force of kinetic friction is proportional
to the normal force between the two surfaces,
and it's proportional to the coefficient
of kinetic friction between the two surfaces.
Note that the force of kinetic friction
does not depend on the velocity of the object.
In other words, if the normal force
and coefficient stay the same,
then no matter how fast or slow the object moves,
no matter how hard or soft you pull,
the force of kinetic friction
is gonna maintain the same value.
Since kinetic friction is a force,
it is a vector and it has units of Newtons.
So what's an example problem
involving kinetic friction look like?
So you've got this question about a car
traveling at cruising speed,
slamming on the brakes, and skidding to a stop.
We want to know what two changes
could be made that would increase the distance required
for the car to skid to a stop.
To get some intuition about what
would cause this car to skid farther,
we could use a kinematic formula.
Since the car skids to a stop,
the final velocity would be zero.
And if we solve for the distance,
we get -v0 squared over two times the acceleration.
So in order to get the car to skid further,
we could increase the initial speed of the car,
or reduce the deceleration.
To figure out what reduces
the magnitude of the acceleration,
we'll use Newton's second law.
The force slowing the skidding car
is the force of kinetic friction,
and since there's no extra vertical forces,
the normal force is just m times g.
Since the masses cancel,
the acceleration won't depend on the mass of the car,
but reducing the coefficient of friction
will reduce the deceleration,
and reducing the deceleration
will increase the distance the car skids to a stop.
The force of static friction tries to prevent
the two surfaces from slipping in the first place,
and that force of static friction will match
whatever force is trying to budge the object
until that budging force matches
the maximum possible static frictional force,
which is proportional to the normal force
and the coefficient of static friction.
So if the maximum value of the
static frictional force is 100 Newtons,
and you try to budge the object with 80 Newtons,
the static frictional force will just oppose you
with 80 Newtons, preventing the object from slipping.
If you exert 90 Newtons, the static frictional force
will increase to 90 Newtons,
preventing the object from slipping.
But if you exert 110 Newtons,
since this exceeds the maximum possible
static frictional force, the object will budge
and there will only be a kinetic frictional force
now that the object is sliding.
So what's an example problem involving
the force of static friction look like?
Let's say you push on a refrigerator that's 180 kilograms,
and the coefficient of static friction
between the floor and the fridge is .8.
If you exert 50 Newtons on the refrigerator,
what's the magnitude of the static friction force
exerted on the refrigerator?
We'll first find the maximum possible
static frictional force using mew s times Fn.
Since there's no extra vertical forces,
the normal force will just be mg.
Plugging in values, we get a maximum possible
static frictional force of 1,411 Newtons,
but this will not be the value
of the static frictional force.
This is just the maximum value
of the static frictional force.
So if we exert 50 Newtons to the right,
since that does not exceed this
maximum possible static frictional force,
static friction will just oppose us
with an equal 50 Newtons to the left.
And it will continue to match whatever force we exert,
until we exceed the maximum
possible static frictional force.
How do you deal with inclines?
Inclines are just angled surfaces that objects
can slide up or down, and since the object
can't move into the incline, or off of the incline,
the motion will only be taking place
parallel to the surface of the incline.
There will be no acceleration perpendicular
to the surface of the incline.
So instead of breaking our forces into x and y,
we break them into forces perpendicular
to the surface and parallel to the surface.
The component of gravity that's parallel
to the surface is gonna equal mg sine theta,
where theta is the angle between the horizontal floor,
and the inclined surface.
And the component of gravity perpendicular
to the surface is gonna be mg cosine theta,
where again, theta is the angle measured between
the horizontal floor and the angled surface.
Since there's no acceleration perpendicular
to the surface, the net force in the
perpendicular direction has to be zero.
And that means this perpendicular component
of gravity has to be exactly canceled
by the normal force, which is why the value
for the normal force is the same
as the perpendicular component of gravity.
And since those perpendicular components cancel,
the total net force on an object on an incline
is just gonna equal the component of the net force
that's parallel to the surface of the incline.
Which, if there's no friction,
would simply be mg sine theta,
and if there was friction,
it would be mg sine theta minus the force of friction.
But be careful when you're finding
the force of friction on an incline,
the normal force will not be m times g,
the normal force is gonna be mg cosine theta.
So what's an example problem involving inclines look like?
Let's say a box started with a huge speed
at the bottom of a frictionless ramp,
and then it slides up the ramp
and through these points shown w, x, y and z.
We want to rank the magnitudes
of the net force on the box
for these points that are indicated.
Well, when the box is flying through the air,
we know the net force is simply the force
of gravity straight down which is m times g.
So the net force at y and z are equal.
And, on an incline, the net force
is the forced component that's parallel
to the surface of the incline,
which is gonna be mg sine theta.
Note that the net force on the incline points down
the incline, even though the mass moves up the incline.
That just means the mass is slowing down,
but since mg is greater than mg sine theta,
z and y are greater than the net force at x and w.
What does treating systems as as single object mean?
This is a trick you can use when
two or more objects are required to move
with the same speed and acceleration,
which will allow us to avoid
having to use multiple equations to find the acceleration,
and instead use one equation to get the acceleration.
When you treat a system of objects
as a single object, you get to ignore internal forces,
since the internal forces will always cancel.
This means you can find the acceleration of the system
by looking at only the external forces on that system,
and then dividing by the total mass of that system.
So what's an example of treating
systems as a single object look like?
Let's say a mass m1 is pulled across a rough
horizontal table by a rope connected to mass m2.
If the coefficient of kinetic friction
between m1 and the table is mew k,
then what's an expression for the
magnitude of the acceleration of the masses?
So instead of analyzing the forces
on each mass individually,
which would give us multiple equations
and multiple unknowns, we'll use one equation
of Newton's second law but we'll treat this system
as if it were a single object.
Which means we're basically just gonna ask
what external forces are gonna make this system go?
And what external forces are gonna make this system stop?
The external force makes this system go
is the force of gravity on m2.
It's an external force, since it's exerted by the Earth,
which is not part of our system,
and it's making the system go,
so we'll call that force positive.
And we'll call forces that try
to make our system stop negative,
like this force of kinetic friction on m1,
which is also external because the table
is not part of the mass of our system.
But we will not include the force of tension,
since this is an internal force,
and these forces will cancel.
Now, since we're treating this system as a single mass,
we'll divide by the total mass of our system.
And then if we write the force of kinetic friction
in terms of the coefficient,
we get mew k times the normal force,
and the normal force on m1 is gonna be m1 times g.
Which, with a single equation, gives us an expression
for the acceleration of our system,
without having to solve multiple equations
with multiple unknowns.