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  • Weve been talking a lot about the science of how things move -- you throw a ball in the air,

  • and there are ways to predict exactly how it will fall.

  • But there’s something weve been leaving out: forces, and why they make things accelerate.

  • And for that, were going to turn to a physicist youve probably heard of: Isaac Newton.

  • With his three laws, published in 1687 in his book Principia, Newton outlined his understanding of motion

  • -- and a lot of his ideas were totally new.

  • Today, more than 300 years later, if youre trying to describe the effects of forces on

  • just about any everyday object -- a box on the ground, a reindeer pulling a sleigh, or

  • an elevator taking you up to your apartment -- then youre going to want to use Newton’s Laws.

  • And yes. I’ll explain the reindeer thing in a minute.

  • [Theme Music]

  • Newton’s first law is all about inertia, which is basically an object’s tendency

  • to keep doing what it’s doing.

  • It’s often stated as: “An object in motion will remain in motion, and an object at rest

  • will remain at rest, unless acted upon by a force.”

  • Which is just another way of saying that, to change the way something moves -- to give

  • it ACCELERATION -- you need a net force.

  • So, how do we measure inertia?

  • Well, the most important thing to know is mass. Say you have two balls that are the

  • same size, but one is an inflatable beach ball and the other is a bowling ball.

  • The bowling ball is going to be harder to move, and harder to stop once it’s moving.

  • It has more inertia because it has more mass.

  • Makes sense, right? More mass means more STUFF, with a tendency to keep doing what it was

  • doing before your force came along, and interrupted it.

  • And this idea connects nicely to Newton’s second law: net force is equal to mass x acceleration.

  • Or, as an equation, F(net) = ma.

  • It’s important to remember that were talking about NET force here -- the amount

  • of force left over, once youve added together all the forces that might cancel each other out.

  • Let's say you have a hockey puck sitting on a perfectly frictionless ice rink. And I know ice isn’t

  • perfectly frictionless but stick with it. If youre pushing the puck along with

  • a stick, that’s a force on it - that isn’t being canceled out by anything else.

  • So the puck is experiencing acceleration.

  • But when the puck is just sitting still, or even when it’s sliding across the ice after

  • youve pushed it, then all the forces are balanced out.

  • That’s what’s known as equilibrium.

  • An object that’s in equilibrium can still be MOVING, like the sliding puck, but its VELOCITY won’t be changing.

  • It’s when the forces get UNbalanced, that you start to see the exciting stuff happen.

  • And probably the most common case of a net force making something move is the gravitational force.

  • Say you throw a 5 kg ball straight up in the air -- and then, yknow, get out of the way,

  • because that could really hurt if it hits you...

  • But the force of gravity is pulling down on the ball, which is accelerating downward at a rate of 9.81 m/s^2.

  • So the net force is equal to m a, but the only force acting here is gravity.

  • This means that, if we could measure the acceleration of the ball, we’d be able to calculate the force of gravity.

  • And we CAN measure the acceleration -- it’s 9.81 m/s^2, the value weve been calling small g.

  • So the force of gravity on the ball must be 5 kg, which is the mass of the balltimes small g

  • which comes to 49.05 kilograms times meters per second squared!

  • We use this equation for gravity so much that it’s often just written as F(g) = mg.

  • That’s how you determine the force of gravity, otherwise known as weight.

  • Now, those units can be a bit of a mouthful, so we just call them Newtons.

  • That’s right! We measure weight in Newtons, in honor of Sir Isaac, and NOT kilograms!

  • Kilograms are a measure of mass!

  • But gravity often isn’t the only force acting on the object.

  • So when were trying to calculate a NET force, we usually have to take into account more than just gravity.

  • 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.

  • You probably know this law asfor every action, there’s an equal but opposite reaction.”

  • Which just means that if you exert a force on an object, it exerts an equal force back on you.

  • And that’s what we call the normal force.

  • Normalin this instance meansperpendicular”, and the normal force is always perpendicular

  • to whatever surface your object is resting on.

  • At least, it is when you're pushing on something big, and macroscopic, like a table.

  • If you put a book down on a table, the normal force is pushing -- and therefore pointing -- up.

  • But if you put it on a ramp, then the normal force is pointing perpendicular to the ramp.

  • Now, the normal force isn’t like most other forces. It’s special, because it changes its magnitude.

  • Say you have a piece of aluminum foil stretched tightly across the top of a bowl, and then

  • you put one lonely grape on top of it.

  • Because of gravity, that grape is exerting a little bit of force on the foil, and the

  • normal force pushes right back, with the same amount.

  • But then you add another grape, which doubles the force on the foil -- in that case, the normal force doubles too.

  • Thatll keep happening until eventually you add enough grapes that they break through the foil.

  • That’s what happens when the normal force can’t match the force pushing against it.

  • But, what does Newton’s famous third law really mean, though?

  • When I push on this desk with my finger right now, I’m applying a force to it.

  • And it’s applying an equal force right back on my finger -- one that I can actually feel.

  • But if that’s true -- and it is -- then why are we able to move things?

  • How can I pick up this mug? Or how can a reindeer pull a sleigh?

  • Basically, things can move because there’s more going on, than just the action and reaction forces.

  • For example, when a reindeer pulls on a sleigh, Newton’s third law tells us that the sleigh

  • is pulling back on it with equal force.

  • But the reindeer can still move the sleigh forward, because it’s standing on the ground.

  • When it takes a step, it’s pushing backward on the ground with its foot -- & the ground is pushing it forward.

  • Meanwhile, the reindeer is also pulling on the sleigh, while the sleigh is pulling right back.

  • But the force from the GROUND PUSHING the reindeer forward is STRONGER than the

  • force from the sleigh pulling it back. So the animal accelerates forward, and so does the sleigh.

  • So, one takeaway here is that: there would be no Christmas without physics!

  • But, now that we have an idea of some of the forces we might encounter, let’s describe

  • what’s happening when a box is sitting on the ground.

  • The first thing to do -- which is the first thing you should ALWAYS do when youre solving

  • a problem like this -- is draw what’s known as a free body diagram.

  • Basically, you draw a rough outline of the object, put a dot in the middle, and then

  • draw and label arrows, to represent all the forces.

  • We also have to decide which direction is positive -- in this case, well choose up to be positive.

  • For our box, the free body diagram is pretty simple. There’s an arrow pointing down,

  • representing the force of gravity, and an arrow pointing up, representing the force

  • of the ground pushing back on the box.

  • Since the box is staying still, we know that it’s not accelerating, which tells us that

  • those forces are equal, so the net force is equal to 0.

  • But what if you attach a rope to the top of the box, then connect it to the ceiling so

  • the box is suspended in the air?

  • Your net force is still 0, because there’s no acceleration on the box. And gravity is

  • still pulling down in the same way it was before.

  • But now, the counteracting upward force comes from the rope acting on the box, in what we call the tension force.

  • To make our examples simpler, we almost always assume that ropes have no mass and are completely

  • unbreakable -- no matter how much you pull on them, theyll pull right back.

  • Which means that the tension force isn’t fixed. If the box weighs 5 Newtons, then the

  • tension in the rope is also 5 Newtons. But if we add another 5 Newtons of weight, the

  • tension in the rope will become 10 Newtons.

  • Kind of like how the normal force changes, with the grapes on the foil. But in this case,

  • it's in response to a pulling force instead of a push.

  • The key is that no matter what, you can add the forces together to give you a particular

  • net force -- even though that net force might NOT always be 0. Like, in an elevator.

  • So let’s say youre in an elevator -- or as I call them, a lift.

  • The total mass of the lift, including you, is 1000 kg. And its movement is controlled

  • by a counterweight, attached to a pulley.

  • The plan is to set up a counterweight of 850kg, and then let the lift go. Once you let go,

  • the lift is going to start accelerating downward - because it’s HEAVIER than the counterweight.

  • And the hope is that the counterweight will keep it from accelerating TOO much.

  • But how will we know if it’s safe? How quickly is the lift going to accelerate downward?

  • To find out, first let’s draw a free body diagram for the lift, making UP the positive direction.

  • The force of gravity on the lift is pulling it down, and it’s equal to the mass of the lift x small g --

  • 9810 Newtons of force, in the negative direction.

  • And the force of tension is pulling the lift UP, in the positive direction.

  • Which means that for the lift, the net force is equal to the tension force, minus the mass of the lift x small g.

  • Now! Since Newton’s first law tells us that F(net) = ma, we can set all of that to be

  • equal to the lift’s mass, times some downward acceleration, -a. That’s what were trying to solve for.

  • So, let’s do the same thing for the counterweight.

  • Gravity is pulling it down with 8338.5 N of force in the negative direction.

  • And again, the force of tension is pulling it up, so that the net force is equal to the

  • tension force, minus the mass of the counterweight times small g.

  • And again, because of Newton’s second law, we know that all of that is equal to the mass

  • of the counterweight, times that same acceleration, “a” -- which is positive this time since

  • the counterweight is moving upward.

  • So! Putting that all together, we end up with two equations -- and two unknowns.

  • We don’t have a value for the tension force, and we don’t have a value for acceleration.

  • But what were trying to solve for is the acceleration. So we use algebra to do that.

  • When you have a system of equations like this, you can add or subtract all the terms on each

  • side of the equals sign, to turn them into one equation.

  • For example, if you know that 1 + 2 = 3 and that 4 + 2 = 6, you can subtract the first

  • equation from the second to get 3 = 3.

  • And in our case, with the lift, subtracting the first equation from the second gets rid

  • of the term that represents the tension force.

  • We now just have to solve for acceleration -- meaning, we need to rearrange the equation to set everything equal to “a.”

  • We end up with an equation that really just says that “a” is equal to the difference

  • between the weights -- or the net force on the system -- divided by the total mass.

  • Essentially, this is just a fancier version of F(net) = ma.

  • And we can solve that for “a”, which turns out to be 0.795 m/s^2.

  • Which is not that much acceleration at all!

  • So, as long as you aren’t dropping too far down, you should be fine.

  • Even if the landing is a little bumpy.

  • In this episode, you learned about Newton’s three laws of motion: how inertia works, that

  • net force is equal to mass x acceleration, how physicists define equilibrium, and all

  • about thenormalforce and thetensionforce.

  • Crash Course Physics is produced in association with PBS Digital Studios. You can head over

  • to their channel to check out amazing shows like: BrainCraft, It’s OK To Be Smart, and PBS Idea Channel.

  • This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course Studio

  • with the help of these amazing people and our Graphics Team is Thought Cafe.

Weve been talking a lot about the science of how things move -- you throw a ball in the air,

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Newton's Laws: Crash Course Physics #5

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    黃齡萱 posted on 2017/07/08
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