跟讀練習: Newton's Laws: Crash Course Physics #5 - 通過影片學習英語口語
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137 句
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We've been talking a lot about the science of how things move.
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You throw a ball in the air, and there are ways to predict exactly how it will fall.
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But there's something we've been leaving out.
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Forces.
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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.
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Isaac Newton.
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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.
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Today, more than 300 years later, if you're trying to describe the effects of forces on just about any everyday object – a box on the ground, a reindeer pulling a sleigh,
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or 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 later.
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Newton's first law is all about inertia.
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Which is basically an object's tendency 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 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 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.
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Say you have two balls that are the 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?
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More mass means more stuff, with a tendency to keep doing what it was doing before your force came along and interrupted it.
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And this idea connects nicely to Newton's second law.
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Net force is equal to mass times acceleration.
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Or, as an equation, F net equals ma.
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It's important to remember that we're talking about net force here, the amount 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.
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And I know they're not usually perfectly frictionless, but stick with it.
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If you're pushing the puck along with 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 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 kilogram ball straight up in the air and then, you know, get out of the way, 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 meters per second squared.
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So the net force is equal to Ma, 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.
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It's 9.81 meters per second squared, the value we've been calling small g.
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So the force of gravity on the ball must be 5 kilograms, which is the mass of the ball, small g, 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 Fg equals 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 in 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, 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 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, the normal force is pointing perpendicular to the ramp.
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Now, the normal force isn't like most other forces.
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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 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 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.
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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, 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?
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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 is pulling back on it with an 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, and 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 force from the sleigh pulling it back.
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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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Now 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.
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The first thing to do, which is the first thing you should always do when you're solving a problem like this, is to 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 draw and label arrows to represent all the forces.
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We also have to decide which direction is positive.
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In this case, we'll choose up to be positive.
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For our box, the free body diagram is pretty simple.
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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.
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Since the box is staying still, we know that it's not accelerating, which tells us that those forces are equal.
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So the net force is equal to zero.
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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?
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Your net force is still zero, because there's no acceleration on the box, and gravity is 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 example simpler, we almost always assume that ropes have no mass and are completely unbreakable.
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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.
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If the box weighs 5 newtons, then the tension in the rope is also 5 newtons.
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But if we add another 5 newtons of weight, the tension in the rope will become 10 newtons.
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It's 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.
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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 zero.
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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 a thousand kilograms, and its movement is controlled by a counterweight attached to a pulley.
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The plan is to set up a counterweight of 850 kilograms, and then let the lift go.
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Once you let go, the lift is going to start accelerating downwards, 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?
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How quickly is the lift going to accelerate downward?
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To find out, let's first 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 times small g.
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9,810 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 times small g.
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Now, since Newton's first law tells us that F net equals ma,
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we can set all of that to be equal to the lift's mass times some downward acceleration, minus a.
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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 8,338.5 Newtons 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 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 of the counterweight times that same acceleration, a, which is positive this time,
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since the counterweight is moving upwards.
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So, putting all of that 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 side of the equals sign to turn them into one equation.
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For example, if you know that 1 plus 2 equals 3, and that 4 plus 2 equals 6,
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you can subtract the first equation from the second to get 3 equals 3.
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And in our case with the lift, subtracting the first equation from the second gets rid 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 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 equals ma.
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And we can solve that for a, which turns out to be 0.795 meters per second squared.
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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's a little bumpy.
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In this episode, you learned about Newton's three laws of motion, how inertia works, that net force is equal to mass times acceleration,
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how physicists define equilibrium, and all about the normal force and the tension force.
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Crash Course Physics is produced in association with PBS Digital Studios.
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You can head over 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 Dr. Cheryl C.
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Kinney's Crash Course Studio with the help of these amazing people and our graphics team is Thought Cafe.
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本課的詞彙與口語要點
這節 C1 級別的口語課以影片“Newton's Laws: Crash Course Physics”為素材。 影片中反覆出現的詞有：force, equal, net, mass, acceleration。 這段影片共有 137 個句子、2220 個單詞可供跟讀。 講話部分時長為 10:50。 說話人語速較快，每分鐘約 205 個詞，會出現較多連讀和弱讀。 83% 的單詞屬於英語最常用的 3,000 詞，其餘的詞建議在練習前先學一下。
影片中的重點詞彙
影片中最難的 15 個單詞，附發音和釋義：
| 單詞 | 發音 | 釋義 |
|---|---|---|
| acceleration 名詞 | /əkˌsɛl.əˈɹeɪ.ʃən/ | 加速 |
| equation 名詞 | /ɪˈkweɪ.ʒən/ | 方程式, 方程 |
| counterweight 名詞 | 配重 | |
| newton 名詞 | /ˈn(j)uːtən/ | 牛頓 /牛頓 |
| kilogram 名詞 | /ˈkɪləɡɹæm/ | 千克, 公斤 |
| reindeer 名詞 | /ˈɹeɪndɪɹ/ | 馴鹿 /馴鹿 |
| accelerate 動詞 | /ɪkˈsɛl.əˌɹeɪt/ | 加速 |
| grape 名詞 | /ɡɹeɪp/ | 葡萄, 提子 |
| foil 名詞 | /fɔɪl/ | 箔 |
| rope 名詞 | /ɹoʊp/ | 繩子 /繩子, 繩索 /繩索 |
| inertia 名詞 | /ɪnˈɝ.ʃə/ | 慣性 /慣性 |
| meter 名詞 | /ˈmitəɹ/ | 計量表 /計量表 |
| exert 動詞 | /ɪɡˈzɝt/ | 施加 |
| perpendicular 形容詞 | /ˌpɜː.pənˈdɪk.jə.lə(ɹ)/ | 垂直 |
| subtract 動詞 | /səbˈtɹækt/ | 減 /減, 減去 /減去 |
影片中出現的短語動詞
| 單詞 | 發音 | 釋義 |
|---|---|---|
| check out 動詞 | 退房 | |
| come along 動詞 | 陪伴, 陪同 | |
| find out 動詞 | 找出, 查明 | |
| make up 動詞 | /ˌmeɪk ˈʌp/ | 組成 /組成 |
| pick up 動詞 | 拾取, 撿 /撿 | |
| show up 動詞 | 露面 |
值得反覆跟讀的句子
影片中簡短而完整的句子，可以直接用在日常對話裡：
- How can I pick up this mug?
- In this case, we'll choose up to be positive.
- But how will we know if it's safe?
- That's what we're trying to solve for.
影片中的語法
說話人最常用的結構，並附上影片中的原話：
| 結構 | 影片中的用法 |
|---|---|
| 現在完成進行時 have/has been + -ing — 以前開始、現在仍在繼續的動作 | We've been talking · we've been leaving · we've been calling |
| 被動語態 be + 過去分詞 — 強調發生了什麼，而不是誰做的 | being canceled · are balanced · is explained |
| 現在完成時 have/has + 過去分詞 — 過去發生但與現在仍有關聯的事 | you've probably heard · you've added · you've pushed |
| 定語從句 who / which + 從句 — 補充說明人或事物 | ball, which is · kilograms, which is · lot, which is |
需要注意的發音
說話人用了 33 次縮略和弱讀形式，例如 you're, we're, isn't。請按聽到的簡短形式來說。
- “sh” 和 “zh” 音: acceleration /əkˌsɛl.əˈɹeɪ.ʃən/, equation /ɪˈkweɪ.ʒən/, inertia /ɪnˈɝ.ʃə/, gravitational /ˌɡɹævɪˈteɪʃənəl/
- 長單詞——注意重音位置: acceleration /əkˌsɛl.əˈɹeɪ.ʃən/, accelerate /ɪkˈsɛl.əˌɹeɪt/, perpendicular /ˌpɜː.pənˈdɪk.jə.lə(ɹ)/, equilibrium /ɛkwɪˈlɪbɹɪəm/, elevator /ˈɛləˌveɪtɚ/
中文母語者容易讀錯的音：
- /v/ — 不要讀成 /w/，上齒輕觸下唇: elevator /ˈɛləˌveɪtɚ/, gravitational /ˌɡɹævɪˈteɪʃənəl/, velocity /vəˈlɑsəti/
- 詞尾子音 — 要讀清楚，後面不要加母音: accelerate /ɪkˈsɛl.əˌɹeɪt/, puck /pʌk/, grape /ɡɹeɪp/, rope /ɹoʊp/, exert /ɪɡˈzɝt/
- /r/ 和 /l/ 的區別: acceleration /əkˌsɛl.əˈɹeɪ.ʃən/, kilogram /ˈkɪləɡɹæm/, accelerate /ɪkˈsɛl.əˌɹeɪt/, perpendicular /ˌpɜː.pənˈdɪk.jə.lə(ɹ)/, equilibrium /ɛkwɪˈlɪbɹɪəm/
如何用這段影片練習
- 先完整聽一遍影片，不要開口，記下不認識的單詞。
- 先用 0.75 倍速逐句跟讀，熟練之後再回到正常速度。
- 錄下自己的聲音並與原聲對比，特別注意 acceleration, equation, counterweight 這類單詞。
什麼是跟讀法？
跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。