Hey there my name is kayleigh and in this lesson, we will learn about Newton's second law
It will be helpful that you've already completed the module called Newton's first law
Do you recall Newton's first law we simplified it to say
objects in motion stay in motion and objects at rest stay at rest unless acted on by an
unbalanced force
Do you remember what happens when an object experiences an unbalanced force
That's right
We'll have a change in speed or direction and this means that there will be a change in velocity
and we define a change in velocity as
acceleration
Now there's a very special relationship
between an object's mass
force and acceleration
It goes like this
The force applied to an object is equal to the mass of the object times the acceleration of the object in
This relationship is what sir Isaac Newton declared as his second law of physics
He said the net force acting on an object is equal to that object's mass times its acceleration
So the force is the magnitude of the
unbalanced force acting on the object
The mass is the objects in
kilogram and the
Acceleration is how fast the object is changing its velocity
so we often write this in shorthand as F equals MA and
It's really convenient to rewrite this equation for acceleration
Where we say a is equal to F over m or the acceleration is equal to force over mass
At this point in this lesson. It's going to be really helpful. If you already have a good understanding of fractions and
with fractions at this point
So let's dig into what these expressions really mean in the real world
if I have two carts with the same mass and
I pull one cart with a big force and one with a small force
What do you think will be different about their accelerations?
We can use the expression solving for acceleration of a equals s over m to think this through
So if the mass is the same for both carts, but one has a big force and the other has a small force
We expect the cart with the larger force the top cart to have a larger acceleration
Well, we can use some numbers to deepen our understanding
So let's say we have two carts and they each have a mass of two kilograms
I'm going to pull the top cart with a force of six Newtons and the bottom cart with only a force of four Newtons
So which one will have a faster acceleration?
We can plug these number into the expression for acceleration
so it goes
For the top one acceleration is equal to six Newton's the force divided by two kilograms the mass and for the bottom cart
Acceleration is equal to a force of four Newton's divided by the same mass of two kilograms
so if I solve for this the top cart will have an acceleration of three meters per second and the bottom cart will have an
Acceleration of two meters per second. So this helps us understand that when two objects have the same mass
The object with the larger force will have a faster acceleration
But what about carts with different masses
So now I'm going to have two carts with different masses and I'm going to pull them with the same force
So what do you think will be different about the accelerations in this example?
We can still use the expression for acceleration
Is equal to force over mass to think this through?
So if they have the same force pulling on them
The heavier cart will accelerate slower than the lighter cart. We can plug them to help us understand
So I'm gonna have my top car is four kilograms and my bottom car is two
Kilograms, and they're both being pulled with a force of eight Newtons
so when I plug those numbers in for the top Kart I get
Acceleration is equal to eight Newton's over four kilograms and the bottom Kart
Acceleration is equal to eight Newton's over two kilograms
so if I do the math for these I'm gonna see the top Kart has an acceleration of two meters per second and
The lighter car is gonna have an acceleration of four meters per second
So we can see when the same force is applied to
two objects with different mass
The object with the lighter mass will accelerate faster than the heavier object
So now what happens if I have two objects with the same acceleration, but different masses
So I know that the
Acceleration is gonna be the same. So they are changing their velocity at the same rate
But what will be different about the forces they're experiencing
So we can use the expression F equals, MA
To help us understand this so the cart with a larger mass and the same acceleration
Will require a larger force to pull it we can plug in some numbers
So let's say the top cart is 3 kilograms
The bottom car is 2 kilograms and they both have an acceleration of 3 meters per second
So I'm going to plug these numbers in for the top car at 3 kilograms times 3 meters per second squared and for the bottom
Cart, the force is 2 kilograms times 3 meters per second squared. So if I complete the math on that
It looks like my top cart is going to be
Requiring a force of 9 Newtons and the lighter cart is going to require a force of 6 Newtons
So now we can see that a cart with a larger mass
Will need to have a larger force applied to it to move with the same acceleration as a longer part
So cool. That's pretty much the gist of Newton's second law
So now let's play a game together so you can watch me play and then you will be able to play on your own
Alright, so here we are in the motion and
forces in motion basics game for acceleration
So first things first, I'm going to click on the acceleration and the speed
For right now, we'll just stick with that just so we can kind of get a hang of what's going on
So in this one, we have a friction slider here. So by sliding it more towards lots
That means there's more friction towards none. There's not no
Lesser friction none it comes iced. So there's nothing for right now
Let's just keep it right in the middle so we can kind of play around
I'm gonna put the girl up here and
Now since there is some friction. It's going to initially take some
applied force to overcome that friction force and then eventually once my forces are
unbalanced we should see our speed increase and we should see acceleration because as we learned
Apply force is equal to the mass of the object times the acceleration
So, let's see what happens
I'm just gonna use my slide bar and we should see the forces so applied force and friction force our balance the
Arrows look the same so still balanced still balanced. No acceleration
Let's see, and I'm starting to
Overcome that friction force and you see immediately the speed is going up. The acceleration has kicked in I'm at
248 Newtons
So if we increase this, what should we see with the acceleration if my force is increasing and my mass is staying the same
I'm going to see an increase in acceleration
Thanks, so I'm gonna let that go so
Now we see the acceleration is negative. The only force is the friction force
So negative right now just means going to the left
Just means the the direction of the direction of motion which we set as right initially
Nice, and now it's all coming to zero because the friction force has balanced out to nothing
Perfect. So, let's see
What happens now if I increase this friction force, so now there's closer to lots
Do you think it's going to take more force to overcome this friction force?
And do you think the acceleration is going to be less?
Or to think it will be the same given that her mass is the same
So this is kind of a tricky one
So when my friction force increases as we'll see I'm going to apply my force and it's going to take more
Apply for us to get her to move initially. Remember at 2:48. We were already moving
We're still not moving. We're still not moving and
Now we're starting at 375. We started to move our acceleration is going our speed is increasing
I'm gonna keep increasing my applied force. So my net force is getting bigger
My unbalanced force is getting bigger. I'm gonna max it out at 500 Newtons
My acceleration is steady and my speed is hitting max speed
So then when my force goes back to zero again only the friction force is acting
Acceleration is going towards the left and my speed is gonna decrease to zero
Awesome
So now if I put this at none
I'm gonna put some values on here. So now we'll see how fast
our speed is and what our acceleration is and
Let's put the man up there. My friction is closer to none. So there should be less friction and
Mass is let's see. So he's eighty kilograms. The box is 50 kilograms
Let's see what happens
So there we saw our friction force and our applied force are now not balanced so I'm gonna have a small acceleration
So my acceleration is 0.35 meters per second squared you'll see my acceleration is constant
But that means that my speed is increasing
Snap. I'm going to increase the
Supplied force what's gonna happen? My acceleration is increasing. So as I increase the force the acceleration increases
And why is that because my mass is constant and F equals, MA
So if M is never changing, but my force is increasing then my acceleration needs to increase
Nice work
We'll see it come all the way my speed is decreasing because I have a friction force
So I'm gonna come all the way back down to zero
And let's just reset this here, so I'm clicking my acceleration on my speed on my
Values my mass is you know everything now
I want you to make a prediction if this box weighs 50 kilograms and
This box also weighs 50 kilograms down here and the girl here weighs 40 kilograms, and I'm going to keep my friction the same
Do you think when I apply 500 Newtons?
So I'm applying a force of 500 Newtons my friction force stays the same
So that means my net force will be the same
Do you think the acceleration of the girl or the acceleration of this box will be more?
So remember the mass here is going to be heavier because 50 plus 50 is gonna be a hundred
Here with 40 and 50 will only be 90
So this combo will have less mass. Do you think with the same force?
The acceleration will be greater for the boxes or the box and the girl
Let's do an experiment. Let's start with the box. I'm putting him up there
so we got a hundred total mass here and I'm gonna take my
Applied force all the way to the 500 here and let's see what happens
all the way to 500
Look at my acceleration is constant here three point one two meters per second squared
Do you remember that three point one two for the box?
Let's reset it three point one two for the box
Let's see what happens I'm putting the girl up there. So now I have 90 kilograms total mass here
I'm going to apply the same amount of force
and will my acceleration be faster than three point one two or slower than sweep wrote one to make your prediction in your head and
I'm sliding it over to 500
and
My acceleration is three point six eight meters per second squared. So that's a greater than it was for the box
and we know
We were able to predict that hopefully right that the girl since she has less mass. This total mass is less and
Objects with lighter mass with the same force applied will have a higher acceleration
Great job
so now it's your turn to play this game on your own so you can check out the practice problems and
Feel free to play around with the simulation
on your own for about five or ten minutes before you try those practice problems to really get a hang of with a slider and
All the buttons and everything means so have fun and remember always be clever