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We’ve been talking a lot about the science of how things move -- you throw a ball in the air,
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and there are ways to predict exactly how it will fall.
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But there’s something we’ve been leaving out: forces, and why they make things accelerate.
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And for that, we’re going to turn to a physicist you’ve probably heard of: Isaac Newton.
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With his three laws, published in 1687 in his book Principia, Newton outlined his understanding of motion
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-- and a lot of his ideas were totally new.
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Today, more than 300 years later, if you’re trying to describe the effects of forces on
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just about any everyday object -- a box on the ground, a reindeer pulling a sleigh, or
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an elevator taking you up to your apartment -- then you’re going to want to use Newton’s Laws.
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And yes. I’ll explain the reindeer thing in a minute.
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[Theme Music]
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Newton’s first law is all about inertia, which is basically an object’s tendency
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to keep doing what it’s doing.
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It’s often stated as: “An object in motion will remain in motion, and an object at rest
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will remain at rest, unless acted upon by a force.”
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Which is just another way of saying that, to change the way something moves -- to give
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it ACCELERATION -- you need a net force.
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So, how do we measure inertia?
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Well, the most important thing to know is mass. Say you have two balls that are the
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same size, but one is an inflatable beach ball and the other is a bowling ball.
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The bowling ball is going to be harder to move, and harder to stop once it’s moving.
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It has more inertia because it has more mass.
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Makes sense, right? More mass means more STUFF, with a tendency to keep doing what it was
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doing before your force came along, and interrupted it.
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And this idea connects nicely to Newton’s second law: net force is equal to mass x acceleration.
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Or, as an equation, F(net) = ma.
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It’s important to remember that we’re talking about NET force here -- the amount
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of force left over, once you’ve added together all the forces that might cancel each other out.
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Let's say you have a hockey puck sitting on a perfectly frictionless ice rink. And I know ice isn’t
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perfectly frictionless but stick with it. If you’re pushing the puck along with
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a stick, that’s a force on it - that isn’t being canceled out by anything else.
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So the puck is experiencing acceleration.
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But when the puck is just sitting still, or even when it’s sliding across the ice after
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you’ve pushed it, then all the forces are balanced out.
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That’s what’s known as equilibrium.
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An object that’s in equilibrium can still be MOVING, like the sliding puck, but its VELOCITY won’t be changing.
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It’s when the forces get UNbalanced, that you start to see the exciting stuff happen.
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And probably the most common case of a net force making something move is the gravitational force.
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Say you throw a 5 kg ball straight up in the air -- and then, yknow, get out of the way,
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because that could really hurt if it hits you...
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But the force of gravity is pulling down on the ball, which is accelerating downward at a rate of 9.81 m/s^2.
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So the net force is equal to m a, but the only force acting here is gravity.
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This means that, if we could measure the acceleration of the ball, we’d be able to calculate the force of gravity.
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And we CAN measure the acceleration -- it’s 9.81 m/s^2, the value we’ve been calling small g.
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So the force of gravity on the ball must be 5 kg, which is the mass of the ball… times small g
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which comes to 49.05 kilograms times meters per second squared!
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We use this equation for gravity so much that it’s often just written as F(g) = mg.
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That’s how you determine the force of gravity, otherwise known as weight.
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Now, those units can be a bit of a mouthful, so we just call them Newtons.
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That’s right! We measure weight in Newtons, in honor of Sir Isaac, and NOT kilograms!
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Kilograms are a measure of mass!
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But gravity often isn’t the only force acting on the object.
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So when we’re trying to calculate a NET force, we usually have to take into account more than just gravity.
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This is where we get into one of the forces that tends to show up a lot, which is explained by Newton’s third law.
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You probably know this law as “for every action, there’s an equal but opposite reaction.”
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Which just means that if you exert a force on an object, it exerts an equal force back on you.
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And that’s what we call the normal force.
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“Normal” in this instance means “perpendicular”, and the normal force is always perpendicular
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to whatever surface your object is resting on.
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At least, it is when you're pushing on something big, and macroscopic, like a table.
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If you put a book down on a table, the normal force is pushing -- and therefore pointing -- up.
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But if you put it on a ramp, then the normal force is pointing perpendicular to the ramp.
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Now, the normal force isn’t like most other forces. It’s special, because it changes its magnitude.
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Say you have a piece of aluminum foil stretched tightly across the top of a bowl, and then
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you put one lonely grape on top of it.
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Because of gravity, that grape is exerting a little bit of force on the foil, and the
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normal force pushes right back, with the same amount.
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But then you add another grape, which doubles the force on the foil -- in that case, the normal force doubles too.
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That’ll keep happening until eventually you add enough grapes that they break through the foil.
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That’s what happens when the normal force can’t match the force pushing against it.
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But, what does Newton’s famous third law really mean, though?
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When I push on this desk with my finger right now, I’m applying a force to it.
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And it’s applying an equal force right back on my finger -- one that I can actually feel.
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But if that’s true -- and it is -- then why are we able to move things?
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How can I pick up this mug? Or how can a reindeer pull a sleigh?
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Basically, things can move because there’s more going on, than just the action and reaction forces.
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For example, when a reindeer pulls on a sleigh, Newton’s third law tells us that the sleigh
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is pulling back on it with equal force.
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But the reindeer can still move the sleigh forward, because it’s standing on the ground.
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When it takes a step, it’s pushing backward on the ground with its foot -- & the ground is pushing it forward.
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Meanwhile, the reindeer is also pulling on the sleigh, while the sleigh is pulling right back.
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But the force from the GROUND PUSHING the reindeer forward is STRONGER than the
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force from the sleigh pulling it back. So the animal accelerates forward, and so does the sleigh.
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So, one takeaway here is that: there would be no Christmas without physics!
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But, now that we have an idea of some of the forces we might encounter, let’s describe
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what’s happening when a box is sitting on the ground.
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The first thing to do -- which is the first thing you should ALWAYS do when you’re solving
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a problem like this -- is draw what’s known as a free body diagram.
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Basically, you draw a rough outline of the object, put a dot in the middle, and then
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draw and label arrows, to represent all the forces.
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We also have to decide which direction is positive -- in this case, we’ll choose up to be positive.
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For our box, the free body diagram is pretty simple. There’s an arrow pointing down,
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representing the force of gravity, and an arrow pointing up, representing the force
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of the ground pushing back on the box.
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Since the box is staying still, we know that it’s not accelerating, which tells us that
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those forces are equal, so the net force is equal to 0.
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But what if you attach a rope to the top of the box, then connect it to the ceiling so
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the box is suspended in the air?
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Your net force is still 0, because there’s no acceleration on the box. And gravity is
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still pulling down in the same way it was before.
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But now, the counteracting upward force comes from the rope acting on the box, in what we call the tension force.
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To make our examples simpler, we almost always assume that ropes have no mass and are completely
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unbreakable -- no matter how much you pull on them, they’ll pull right back.
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Which means that the tension force isn’t fixed. If the box weighs 5 Newtons, then the
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tension in the rope is also 5 Newtons. But if we add another 5 Newtons of weight, the
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tension in the rope will become 10 Newtons.
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Kind of like how the normal force changes, with the grapes on the foil. But in this case,
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it's in response to a pulling force instead of a push.
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The key is that no matter what, you can add the forces together to give you a particular
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net force -- even though that net force might NOT always be 0. Like, in an elevator.
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So let’s say you’re in an elevator -- or as I call them, a lift.
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The total mass of the lift, including you, is 1000 kg. And its movement is controlled
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by a counterweight, attached to a pulley.
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The plan is to set up a counterweight of 850kg, and then let the lift go. Once you let go,
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the lift is going to start accelerating downward - because it’s HEAVIER than the counterweight.
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And the hope is that the counterweight will keep it from accelerating TOO much.
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But how will we know if it’s safe? How quickly is the lift going to accelerate downward?
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To find out, first let’s draw a free body diagram for the lift, making UP the positive direction.
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The force of gravity on the lift is pulling it down, and it’s equal to the mass of the lift x small g --
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9810 Newtons of force, in the negative direction.
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And the force of tension is pulling the lift UP, in the positive direction.
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Which means that for the lift, the net force is equal to the tension force, minus the mass of the lift x small g.
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Now! Since Newton’s first law tells us that F(net) = ma, we can set all of that to be
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equal to the lift’s mass, times some downward acceleration, -a. That’s what we’re trying to solve for.
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So, let’s do the same thing for the counterweight.
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Gravity is pulling it down with 8338.5 N of force in the negative direction.
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And again, the force of tension is pulling it up, so that the net force is equal to the
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tension force, minus the mass of the counterweight times small g.
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And again, because of Newton’s second law, we know that all of that is equal to the mass
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of the counterweight, times that same acceleration, “a” -- which is positive this time since
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the counterweight is moving upward.
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So! Putting that all together, we end up with two equations -- and two unknowns.
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We don’t have a value for the tension force, and we don’t have a value for acceleration.
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But what we’re trying to solve for is the acceleration. So we use algebra to do that.
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When you have a system of equations like this, you can add or subtract all the terms on each
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side of the equals sign, to turn them into one equation.
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For example, if you know that 1 + 2 = 3 and that 4 + 2 = 6, you can subtract the first
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equation from the second to get 3 = 3.
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And in our case, with the lift, subtracting the first equation from the second gets rid
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of the term that represents the tension force.
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We now just have to solve for acceleration -- meaning, we need to rearrange the equation to set everything equal to “a.”
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We end up with an equation that really just says that “a” is equal to the difference
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between the weights -- or the net force on the system -- divided by the total mass.
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Essentially, this is just a fancier version of F(net) = ma.
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And we can solve that for “a”, which turns out to be 0.795 m/s^2.
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Which is not that much acceleration at all!
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So, as long as you aren’t dropping too far down, you should be fine.
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Even if the landing is a little bumpy.
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In this episode, you learned about Newton’s three laws of motion: how inertia works, that
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net force is equal to mass x acceleration, how physicists define equilibrium, and all
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about the “normal” force and the “tension” force.
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Crash Course Physics is produced in association with PBS Digital Studios. You can head over
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to their channel to check out amazing shows like: BrainCraft, It’s OK To Be Smart, and PBS Idea Channel.
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This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course Studio
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with the help of these amazing people and our Graphics Team is Thought Cafe.