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# Newton's second law of motion

Newton's second law of motion states that F = ma, or net force is equal to mass times acceleration. A larger net force acting on an object causes a larger acceleration, and objects with larger mass require more force to accelerate. Both the net force acting on an object and the object's mass determine how the object will accelerate. Created by Sal Khan.

## Want to join the conversation?

- Why is it valuable to recognize scalar and vector values? I understand the difference between them, but I don't understand the practicality of it. Thanks.(50 votes)
- let's say your driving North at 50 mph for an hour (which is a vector because it has a magnitude, 50mph, and a direction, North), then you know you went 50 miles North, rather than just 50 miles in ay direction, and if you're like me then you might want to know which direction you're driving in.(76 votes)

- what exactly is a vector force?(20 votes)
- You might want to watch this video on vector and scalars:

http://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/introduction-to-vectors-and-scalars

Hope this helps,

Yamu(30 votes)

- I understand the whole math part of the formula (it's pretty simple), but can anyone tell me what he means by 5 m/s^2? is it just saying that this object of mass is moving at a speed of 5 meters per second? Why is seconds squared?(13 votes)
- 5 meters per second is a rate, but acceleration is a change in rate, so 5 meters per second per second. this would look like 5m/sec/sec. If you apply algebra to this, that would be the same as 5m/sec *1/sec, because dividing is the same as multiplying by the reciprocal. multiply it out and you get 5m/sec^2.(22 votes)

- how do objects hit the floor at the same time(5 votes)
- HI Jorge Garcia,

This only stands true when there is no air resistance present.

Suppose that an bowling ball and a tennis ball are dropped off a cliff at the same time. To understand this we must use Newton's second law - the law of acceleration (acceleration = force/mass). Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. Acceleration of an object depends on two things, force and mass. This shows that the bowling experiences a much greater force. But because of the big mass, it resists acceleration more. Even though a bowling ball may experience 100 times the force of a tennis ball, it has 100 times the mass. So, the force/mass ratio (from the equation acceleration = force/mass) is the same for each. Therefore, the acceleration is the same and they reach the ground at the same time.

Hope that helps!

- JK(15 votes)

- hi there , I had a doubt in newtons laws of motion could you pls help me .....

a person kicks a 1kg football to score a goal. When he kicks a 1kg brick , his foot gets hurt .give a reason for it. thank you(4 votes)- What happens to the shape of the football and the brick when kicked? The football deforms and then elastically rebounds where as the brick is rigid and doesn't deform.

The deformation of the football increases the amount of time that the force of the kick is spread out so to transfer the momentum from the foot to the football is done at a slower rate over a longer time requiring a lower force.

The brick being rigid the momentum transfer has to occur quicker so there is more force on the foot and brick making it more painful and more likely to cause damage to the foot.(17 votes)

- Am I correct?

F ∝ M & F ∝ A & Multiplication represents proportionality, and therefore F = M * A.

A better way to visualize everything is through A = F / M. Logically, doubling the force upon an object will double the acceleration of the object.

The unit kg * m/s^2 cannot be comprehended as kg * m/s^2 because you have created a new unit out of two independent properties: mass & acceleration. Kg * m/s^2 is a new unit that represents force, right?(7 votes)- You are correct. a = F / m is just an easier alternate form, because mass typically doesn't change in a lot of force problems. kg * m / s^2 is the unit of force called Newton. Just to slightly nitpick, it's usually better to write acceleration as lowercase a, to avoid confusion with area (A).(8 votes)

- why is force=massxacceleration(6 votes)
- That's how force is defined based on experimental observations.(7 votes)

- can we find what the mass of an object is if we know the force and the acceleration of that object just like how we found the acceleration because we knew the force and mass of that object?(4 votes)
- Yes! If you know two parts of an equation with three variables, you can find the remaining variable's value.(9 votes)

- I don't get one thing.

In the 1d motion I learnt that 2 objects irrespective of their mass will fall with the same velocity. But, according to the 2nd law of motion i.e. F=ma, force on a body is directly proportional to it's mass. And more the force, the greater the velocity of the object.

Please explain.(5 votes)- F = mg (this says that the pull is stronger on a heavier object)

And

F = ma (this says it takes more pull to accelerate heavier object)

So ma = mg

m cancels out

a = g(6 votes)

- so, to clarify, the direction of net force and acceleration will always be the same?(4 votes)
- That is correct - it the force that produces the acceleration. The velocity might be in any direction, but the acceleration will be in the same direction. (I'm racking my brain to see if there might be a counter example and - well - nothing so far :-)(6 votes)

## Video transcript

Newton's First Law tells
us that an object at rest will stay at rest, and object
with a constant velocity will keep having that
constant velocity unless it's affected by
some type of net force. Or you actually could say an
object with constant velocity will stay having a
constant velocity unless it's affected
by net force. Because really, this
takes into consideration the situation where
an object is at rest. You could just have
a situation where the constant velocity is zero. So Newton's First
Law, you're going to have your constant velocity. It could be zero. It's going to stay being
that constant velocity unless it's affected,
unless there's some net force that acts on it. So that leads to the
natural question, how does a net force affect
the constant velocity? Or how does it affect of
the state of an object? And that's what Newton's
Second Law gives us. So Newton's Second
Law of Motion. And this one is maybe
the most famous. They're all kind of
famous, actually. I won't pick favorites here. But this one gives us
the famous formula force is equal to mass
times acceleration. And acceleration is
a vector quantity, and force is a vector quantity. And what it tells us--
because we're saying, OK, if you apply
a force it might change that constant velocity. But how does it change
that constant velocity? Well, let's say I have
a brick right here, and it is floating in space. And it's pretty nice for us
that the laws of the universe-- or at least in the classical
sense, before Einstein showed up-- the laws of
the universe actually dealt with pretty simple mathematics. What it tells us is if
you apply a net force, let's say, on this
side of the object-- and we talk about net force,
because if you apply two forces that cancel out and that
have zero net force, then the object won't change
its constant velocity. But if you have a
net force applied to one side of this
object, then you're going to have a net acceleration
going in the same direction. So you're going to have
a net acceleration going in that same direction. And what Newton's
Second Law of Motion tells us is that acceleration
is proportional to the force applied, or the force
applied is proportional to that acceleration. And the constant
of proportionality, or to figure out what you have
to multiply the acceleration by to get the force, or what you
have to divide the force by to get the acceleration,
is called mass. That is an object's mass. And I'll make a
whole video on this. You should not confuse
mass with weight. And I'll make a whole
video on the difference between mass and weight. Mass is a measure of
how much stuff there is. Now, that we'll
see in the future. There are other things
that we don't normally consider stuff that
does start to have mass. But for our classical, or at
least a first year physics course, you could
really just imagine how much stuff there is. Weight, as we'll see
in a future video, is how much that stuff
is being pulled down by the force of gravity. So weight is a force. Mass is telling you how
much stuff there is. And this is really neat that
this formula is so simple, because maybe we could have
lived in a universe where force is equal to mass squared
times acceleration times the square root of acceleration,
which would've made all of our math much
more complicated. But it's nice. It's just this constant
of proportionality right over here. It's just this nice
simple expression. And just to get our feet wet
a little bit with computations involving force, mass,
and acceleration, let's say that I have a force. And the unit of force
is appropriately called the newton. So let's say I have a
force of 10 newtons. And just to be clear, a
newton is the same thing as 10 kilogram meters
per second squared. And that's good that a newton
is the same thing as kilogram meters per second squared,
because that's exactly what you get on this side of the formula. So let's say I have a
force of 10 newtons, and it is acting on a mass. Let's say that the
mass is 2 kilograms. And I want to know
the acceleration. And once again, in this video,
these are vector quantities. If I have a positive
value here, we're going to make the assumption
that it's going to the right. If I had a negative value, then
it would be going to the left. So implicitly I'm
giving you not only the magnitude of the
force, but I'm also giving you the direction. I'm saying it is to the
right, because it is positive. So what would be acceleration? Well we just use f equals ma. You have, on the
left hand side, 10. I could write 10
newtons here, or I could write 10 kilogram
meters per second squared. And that is going to be
equal to the mass, which is 2 kilograms times
the acceleration. And then to solve
for the acceleration, you just divide both
sides by 2 kilograms. So let's divide the
left by 2 kilograms. Let me do it this way. Let's divide the
right by 2 kilograms. That cancels out. The 10 and the 2, 10
divided by 2 is 5. And then you have kilograms
canceling with kilograms. Your left hand side, you get
5 meters per second squared. And then that's equal
to your acceleration. Now just for fun, what happens
if I double that force? Well then I have 20 newtons. Well, I'll actually work it out. Then I have 20 kilogram
meters per second squared is equal to-- I'll
have to color code-- 2 kilograms times
the acceleration. Divide both sides by 2
kilograms, and what do we get? Cancels out. 20 divided by 2 is 10. Kilograms cancel kilograms. And so we have the
acceleration, in this situation, is equal to 10 meters
per second squared is equal to the acceleration. So when we doubled the force--
we went from 10 newtons to 20 newtons-- the
acceleration doubled. We went from 5 meters
per second squared to 10 meters per second squared. So we see that they are
directly proportional, and the mass is that how
proportional they are. And so you could imagine what
happens if we double the mass. If we double the mass in this
situation with 20 newtons, then we won't be dividing
by 2 kilograms anymore. We'll be dividing
by 4 kilograms. And so then we'll have 20
divided by 4, which would be 5 and would be meters
per second squared. So if you make the mass
larger, if you double it, then your acceleration
would be half as much. So the larger the mass
you have, the more force you need to accelerate it. Or for a given force, the less
that it will accelerate it, the harder it is to change
its constant velocity.