AP Physics 1 review of Forces and Newton's Laws | Physics | Khan Academy

- [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.