Motion, Forces & Energy
IGCSE Physics Topic 1 22:00 English narration · English + 中文 subtitles burned in
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Transcript
Look around you.
看看你周围。
A car speeds up. A ball drops. A cup sits still on a table.
汽车加速，球落下，杯子静静地放在桌上。
Physics can describe every one of these — exactly, using numbers.
物理学能精确地、用数字描述这一切。
And it all rests on three big ideas: how things move, the forces that push and pull them, and the energy that flows between them.
而这一切都建立在三个重要概念之上：物体如何运动，推和拉它们的力，以及在它们之间流动的能量。
This is where physics begins: motion, forces, and energy.
物理学就从这里开始：运动、力和能量。
Get these foundations right, and the rest of the course will follow.
把这些基础打牢，课程的其余部分就会水到渠成。
Let's start.
让我们开始吧。
Every measurement in physics needs a unit.
物理学中的每个测量都需要一个单位。
Length is measured in metres, mass in kilograms, and time in seconds.
长度用米，质量用千克，时间用秒。
And every quantity is one of two types.
而每个物理量都属于两类之一。
A scalar has magnitude — size — only, like distance, speed, and mass.
标量只有大小——比如距离、速率和质量。
A vector has magnitude and a direction — like force, velocity, and momentum.
矢量既有大小又有方向——比如力、速度和动量。
That one extra word, direction, will matter again and again.
方向这个词，会一次又一次地起作用。
Start with measuring.
我们从测量开始。
Use a ruler for length, and put your eye straight in front of the mark — looking from the side gives a wrong reading.
长度用直尺量，而且眼睛要正对着刻度看——从侧面看会读错。
Use a measuring cylinder for the volume of a liquid, and read the bottom of the curved surface, called the meniscus, with your eye level with it.
液体的体积用量筒量，要读弯曲液面的最低点，也就是弯月面，眼睛要与它齐平。
Now the important trick.
现在讲那个重要的窍门。
A single small length, or one short time, is hard to measure well.
单独一个很小的长度，或者一段很短的时间，都很难量准。
So measure many and divide.
所以要多量几个再除。
To find the thickness of one page, measure a hundred pages and divide by a hundred.
要测一张纸的厚度，就量一百张再除以一百。
To find the time for one swing of a pendulum, time twenty swings and divide by twenty.
要测摆的一次摆动时间，就给二十次摆动计时再除以二十。
One full swing is called the period.
一次完整的摆动叫做周期。
This makes the uncertainty — the size of your error — much smaller.
这样做能让不确定度——也就是误差的大小——小得多。
Two forces can act at right angles to each other.
两个力可以互相成直角作用。
To combine them, draw each as a side of a rectangle.
要把它们合成，就把每个力画成矩形的一条边。
The single force that could replace both is called the resultant — the diagonal of that rectangle.
能同时替代这两个力的那一个力，叫做合矢量——也就是矩形的对角线。
We find how big it is using Pythagoras, and which way it points using trigonometry.
我们用勾股定理求出它的大小，用三角函数求出它的方向。
Speed is the distance travelled per unit time — v equals s over t.
速率是单位时间内走过的距离——v 等于 s 除以 t。
If the speed changes during a journey, use average speed: the total distance divided by the total time, not the average of the speeds.
如果一段路程中速率有变化， 就用平均速率：总距离除以总时间，而不是把各个速率平均一下。
Velocity is speed in a stated direction.
速度是带有指定方向的速率。
That one extra word matters: velocity is a vector and speed is a scalar.
多出来的这几个字很重要：速度是矢量，速率是标量。
And acceleration is the change in velocity per unit time — a equals delta v over delta t, where delta v means the change in velocity.
而加速度是单位时间内速度的变化——a 等于 delta v 除以 delta t， 其中 delta v 表示速度的变化量。
Slowing down is called deceleration, and it is simply a negative acceleration.
变慢叫做减速，它不过就是负的加速度。
A car speeds up from eight metres per second to twenty metres per second in four point zero seconds.
一辆汽车在四点零秒内从每秒八米加速到每秒二十米。
Find its acceleration.
求它的加速度。
First the change in velocity: twenty minus eight is twelve metres per second.
先求速度的变化：二十减八等于十二米每秒。
Then divide by the time: twelve over four point zero.
再除以时间：十二除以四点零。
The answer is three point zero metres per second squared.
答案是三点零米每二次方秒。
Watch the unit — metres per second SQUARED, because it is metres per second, per second.
注意单位——是米每二次方秒， 因为它是每秒每秒增加多少米每秒。
Graphs let us read motion at a glance.
图像让我们一眼就能读出运动。
First, a distance–time graph.
先看距离–时间图。
A flat line means the object is not moving.
水平线表示物体没有移动。
A straight slope means a steady speed — and the steeper the line, the faster it goes.
直的斜线表示匀速——线越陡，走得越快。
Here, the gradient is the speed.
在这里，斜率就是速率。
Now a speed–time graph.
再看速度–时间图。
On this one, the gradient is something new: the acceleration.
在这张图上，斜率是新的东西：加速度。
And the area under the line gives the distance travelled.
而线下的面积给出走过的距离。
Read each graph carefully — they are not the same.
仔细看每张图——它们并不一样。
Near the Earth, all objects fall with the same acceleration — about ten metres per second, every second.
在地球附近，所有物体下落时都有相同的加速度——大约每秒每秒十米。
But the air pushes back.
但空气会往回推。
As the object falls faster, this air resistance grows.
物体下落得越快，这个空气阻力就越大。
When the air resistance becomes equal to the weight, the two forces balance.
当空气阻力等于重力时，两个力相互平衡。
The object stops speeding up and falls at a steady speed.
物体不再加速，以稳定的速度下落。
We call this the terminal velocity.
我们把它叫做收尾速度。
A distance-time graph shows how far something has gone.
距离时间图显示物体走了多远。
Three shapes to recognise.
有三种形状要认得。
A flat horizontal line means the object is at rest — time passes but the distance does not change.
一条水平的直线表示物体静止—— 时间在走，距离却不变。
A straight slope means constant speed, and the gradient, the steepness, IS the speed: steeper means faster.
一条倾斜的直线表示匀速，而斜率、也就是陡峭程度， 就是速率：越陡越快。
A curve that gets steeper means the object is speeding up, because the gradient is increasing.
一条越来越陡的曲线表示物体在加速，因为斜率在变大。
So on this graph you find speed by measuring the gradient.
所以在这张图上，你是通过量斜率来求速率的。
A speed-time graph looks similar but means something completely different, and mixing them up is the commonest mistake in this topic.
速率时间图看上去很像，含义却完全不同，而把两者搞混是本章最常见的错误。
Here a flat line means constant SPEED — not at rest.
在这里，一条水平线表示匀速——不是静止。
A straight slope means constant acceleration, and the gradient is the acceleration, not the speed.
一条倾斜的直线表示匀加速， 而斜率是加速度，不是速率。
And this graph has an extra property: the AREA under the line is the distance travelled.
而且这张图还多了一个性质：线下的面积就是走过的距离。
So on a distance-time graph you measure the gradient to get speed; on a speed-time graph you measure the gradient to get acceleration, and the area to get distance.
所以在距离时间图上，你量斜率得到速率；在速率时间图上， 你量斜率得到加速度，量面积得到距离。
Never read one as if it were the other.
千万不要把一张图当成另一张来读。
Near the Earth, all objects speed up as they fall at the same rate — the acceleration of free fall, g, about nine point eight metres per second squared.
在地球附近，所有物体下落时加速的快慢都一样——这就是自由落体加速度 g， 约为九点八米每二次方秒。
But when something falls through air, air resistance pushes upward on it, and here is the key idea: air resistance GROWS as the object goes faster.
但当物体在空气中下落时，空气阻力会向上推它， 而关键的想法在这里：物体越快，空气阻力就越大。
Just after release the weight is much bigger than the air resistance, so the object accelerates.
刚放手时，重力远大于空气阻力， 所以物体加速。
As it speeds up, the air resistance builds.
随着速度变快，空气阻力不断增大。
Eventually the air resistance equals the weight.
最终空气阻力等于重力。
Now the resultant force is zero, so it stops speeding up — and it falls at a steady terminal velocity.
这时合力为零，于是它不再加速——它以恒定的收尾速度下落。
Note it does not slow down and it does not stop; it keeps falling, just at a constant speed.
注意它并没有变慢，也没有停下；它仍在下落，只是速度不变了。
Hang a load on a spring and it stretches.
在弹簧上挂一个重物，它就会伸长。
The stretch is called the extension — and that word matters, because extension means the stretched length minus the ORIGINAL length, not the whole length.
这个伸长叫做伸长量—— 而这个词很重要，因为伸长量指的是拉伸后的长度减去原来的长度，不是整个长度。
On a load-extension graph the line is straight at first: extension is proportional to load, and that is Hooke's law.
在载荷伸长图上，线一开始是直的：伸长量与载荷成正比，这就是胡克定律。
The point where it stops being straight is the limit of proportionality.
直线开始弯曲的那一点，叫做比例极限。
Past that point, the simple relationship no longer holds.
过了那一点，这个简单的关系就不再成立了。
The spring constant is the force per unit extension, k equals F over x, and a large k means a stiff spring.
弹簧常数是每单位伸长量所需的力，k 等于 F 除以 x，k 越大，弹簧越硬。
A force is a push or a pull.
力是推或拉。
Add up all the forces on an object to find the resultant force.
把物体受到的所有力加起来，得到合力。
If it is zero, the object stays still, or moves at a steady speed in a straight line.
如果合力为零， 物体就保持静止，或者沿直线匀速运动。
If it is not zero, the object accelerates, and the force equals mass times acceleration.
如果合力不为零，物体就加速， 而力等于质量乘以加速度。 我们来试一试。
Let's try it. A car feels a resultant force of two thousand four hundred newtons. Its mass is twelve hundred kilograms.
一辆汽车受到两千四百牛顿的合力， 它的质量是一千二百千克。
So its acceleration is two metres per second, every second.
所以它的加速度是每秒每秒两米。
A free-body diagram shows every force on an object as a labelled arrow.
受力图把作用在物体上的每一个力都画成一个带标注的箭头。
Here: the weight down, the normal force from the ground up, a push to the right and friction to the left.
这里有：向下的重力、地面向上的支持力、向右的推力和向左的摩擦力。
To find the resultant force, add forces along a straight line, counting one direction as positive and the other as negative.
要求合力，就把沿同一直线的力加起来，一个方向记为正，另一个方向记为负。
Then two rules.
然后有两条规则。
If the resultant force is zero, the object either stays at rest OR keeps moving in a straight line at constant speed — that is Newton's first law, and notice it allows movement.
如果合力为零，物体要么保持静止， 要么沿直线以恒定速率继续运动——这就是牛顿第一定律，注意它是允许运动的。
If the resultant force is not zero, the object accelerates in the direction of that force, and F equals m a.
如果合力不为零，物体就沿着这个力的方向加速，而且 F 等于 m a。
A twelve hundred kilogram car has a three thousand newton driving force and six hundred newtons of friction.
一辆一千二百千克的汽车有三千牛顿的驱动力和六百牛顿的摩擦力。
Find its acceleration.
求它的加速度。
Find the resultant force first — that is the step people skip.
先求合力——这一步正是人们会跳过的。
Three thousand minus six hundred is two thousand four hundred newtons.
三千减六百等于二千四百牛顿。
Then a equals F over m: two thousand four hundred over twelve hundred, which is two point zero metres per second squared.
然后 a 等于 F 除以 m：二千四百除以一千二百，等于二点零米每二次方秒。
And a word on that friction: friction is the force between two surfaces that touch.
再说说摩擦力：摩擦力是两个接触表面之间的力。
It opposes motion and it makes things heat up.
它阻碍运动，还会让物体发热。
Drag — friction in a liquid or a gas, like air resistance — does the same job.
阻力——液体或气体中的摩擦，比如空气阻力——起的是同样的作用。
Forces can also turn things.
力还能让物体转动。
The moment of a force is its turning effect about a pivot.
一个力的力矩，是它绕支点的转动效果。
It equals the force times the perpendicular distance from the pivot.
它等于力乘以到支点的垂直距离。
When something is in equilibrium, the total clockwise moment equals the total anticlockwise moment and the forces balance too.
当物体平衡时，总的顺时针力矩等于总的逆时针力矩，各个力也互相平衡。
This is the principle of moments.
这就是力矩原理。
A wide base and a low centre of gravity also help an object stay stable, so it does not topple over.
宽的底座和低的重心也能帮助物体保持稳定，不容易翻倒。
A thirty newton weight sits nought point two zero metres to the left of a pivot.
一个三十牛顿的重物放在支点左边零点二零米处。
How far to the right must a twenty newton weight sit to balance the beam?
要让横梁平衡， 一个二十牛顿的重物必须放在右边多远处？
Because it is balanced, use the principle of moments: total clockwise moment equals total anticlockwise moment.
因为它是平衡的，就用力矩原理： 顺时针力矩的总和等于逆时针力矩的总和。
Put the numbers in: thirty times nought point two zero equals twenty times d.
把数字代进去： 三十乘以零点二零，等于二十乘以 d。
That gives six point zero equals twenty d, so d is nought point three zero metres.
得到六点零等于二十 d，所以 d 是零点三零米。
Check it makes sense — the lighter weight has to sit further out, and it does.
检查一下是否合理——较轻的那个重物必须放得更远，而结果正是如此。
The centre of gravity is the single point where all the weight of an object seems to act.
重心是物体的全部重量看起来集中作用的那一个点。
To find it for a flat shape, called a lamina: hang it from a pin and let it settle, then draw a vertical line down from the pin using a plumb line.
对一个叫做薄片的平面形状，要找出它的重心：用一根针把它悬挂起来，等它静止， 再用铅垂线从针那里向下画一条竖直线。
Repeat from a different point.
换一个点再做一次。
Where the lines cross is the centre of gravity.
两条线的交点就是重心。
Now stability.
再说稳定性。
An object is more stable when it has a low centre of gravity and a wide base.
当物体的重心低、底面宽时，它更稳定。
And here is the actual rule for when it falls: it tips over when the centre of gravity passes outside the base.
而它到底什么时候会倒，规则是这样的：当重心越出底面范围时，它就会翻倒。
That is why a racing car is low and wide, and why a tall thin vase falls so easily.
这正是赛车又低又宽的原因，也是又高又细的花瓶那么容易倒的原因。
Density is the mass per unit volume — rho equals m over V, where rho is the Greek letter "rho".
密度是单位体积的质量——rho 等于 m 除以 V，其中 rho 是希腊字母"柔"。
The unit is kilograms per cubic metre, or grams per cubic centimetre.
单位是千克每立方米，或者克每立方厘米。
To find it, measure the mass with a balance, find the volume, then divide.
要求它，就用天平量出质量， 求出体积，再相除。
For a regular solid like a box, measure the sides and calculate.
对像盒子这样的规则固体，量出各边长再计算。
For an irregular solid, lower it into water in a measuring cylinder — the rise in the water level is its volume.
对不规则固体，把它放进装水的量筒里——水位上升的那部分就是它的体积。
That is the displacement method.
这就是排水法。
And the rule for floating: an object floats if its density is LESS than the density of the liquid, and sinks if it is greater.
而漂浮的规则是：如果物体的密度小于液体的密度，它就漂浮； 大于就下沉。
Ice is only slightly less dense than water, which is exactly why an iceberg floats with almost all of itself hidden below the surface.
冰的密度只比水略小一点点，这正是冰山漂浮时， 几乎整个身子都藏在水面以下的原因。
A stone of mass fifty-four grams is lowered into a measuring cylinder.
一块质量为五十四克的石头被放进量筒。
The water level rises from twenty to forty cubic centimetres.
水位从二十立方厘米升到四十立方厘米。
Find the density of the stone.
求石头的密度。
The volume of the stone is the rise in the water level — forty minus twenty, which is twenty cubic centimetres, NOT forty.
石头的体积是水位上升的那一部分——四十减二十， 也就是二十立方厘米，而不是四十。
Then rho equals m over V: fifty-four over twenty, which is two point seven grams per cubic centimetre.
然后 rho 等于 m 除以 V： 五十四除以二十，等于二点七克每立方厘米。
Notice the units follow the numbers you used: grams and cubic centimetres in, grams per cubic centimetre out.
注意单位是跟着你代进去的数字走的：进去的是克和立方厘米，出来的就是克每立方厘米。
Mass is the amount of matter in an object, measured in kilograms. It never changes.
质量是物体中物质的多少，用千克来量，它永远不变。
Weight is different: it is the pull of gravity, measured in newtons, and it is weaker on the Moon.
重力不同： 它是重力的拉力，用牛顿来量，在月球上更小。
Density tells us how tightly matter is packed — the mass divided by the volume.
密度告诉我们物质挤得有多紧—— 就是质量除以体积。
To measure the volume of an odd shape, lower it into water and see how far the level rises.
要量一个不规则形状的体积，把它放进水里，看水面升高多少。
A stone of fifty-four grams pushes the water up by twenty cubic centimetres, so its density is about two point seven grams per cubic centimetre.
一块五十四克的石头把水顶高二十立方厘米，所以它的密度约为每立方厘米二点七克。
If an object is less dense than the liquid, it floats.
如果物体比液体密度小，它就会漂浮。
Momentum is mass times velocity, and it is a vector.
动量是质量乘以速度，它是一个矢量。
Here is why it is useful.
它为什么有用呢？
When objects push on each other, and nothing from outside interferes, the total momentum stays the same — before and after.
当物体相互推挤、而外界又没有干扰时，总动量保持不变——碰撞前后都一样。
Watch.
看。
A two-kilogram trolley moving at three metres per second hits a one-kilogram trolley at rest, and they stick together.
一辆两千克的小车以每秒三米撞上一辆静止的一千克小车，它们粘在一起。
The momentum before is six.
碰撞前的动量是六。
Afterwards, that same six is shared by three kilograms.
碰撞后，同样的六由三千克来分。
So they move off together at two metres per second.
所以它们一起以每秒两米移动。
Momentum is mass times velocity, p equals m v, and it is a vector — so direction counts.
动量是质量乘以速度，p 等于 m v，而且它是矢量——所以方向是要算的。
Impulse is the force times the time it acts, and it equals the change in momentum.
冲量是力乘以它作用的时间，而它等于动量的变化量。
Rearranged, that says the resultant force is the change in momentum per unit time: F equals delta p over delta t.
移项之后就是说， 合力等于单位时间内动量的变化：F 等于 delta p 除以 delta t。
Now look at what that means in practice, because it explains a lot of safety engineering.
现在看看这在实际中意味着什么，因为它解释了大量的安全工程。
The change in momentum in a crash is fixed — you are going to stop either way.
碰撞中动量的变化量是定死的——反正你都要停下来。
But if you can make the stopping TIME longer, the force must be smaller.
但如果你能把停下来的时间拉长，力就必须变小。
That is exactly what an airbag, a crumple zone and a crash helmet all do.
安全气囊、溃缩区和头盔做的正是这件事。
A two point zero kilogram trolley moving at three point zero metres per second hits a stationary one point zero kilogram trolley, and they stick together.
一辆二点零千克的小车以每秒三点零米撞上一辆静止的一点零千克小车，两车粘在一起。
Find their common velocity afterwards.
求它们之后共同的速度。
Momentum is conserved, so work out the total momentum before: two point zero times three point zero, plus one point zero times zero — the stationary one contributes nothing — which is six kilogram metres per second.
动量守恒，所以先算出碰撞前的总动量： 二点零乘以三点零，加上一点零乘以零——静止的那辆什么也不贡献—— 得到六千克米每秒。
Afterwards they stick together, so they move as one object of mass three point zero kilograms.
碰撞后它们粘在一起，所以作为一个三点零千克的整体运动。
Six equals three point zero v, so v is two point zero metres per second.
六等于三点零 v，所以 v 是二点零米每秒。
Energy can be stored in different ways, and you should be able to name them: kinetic, gravitational potential, chemical, elastic, nuclear, electrostatic, and internal or thermal.
能量可以以不同的方式储存，而你应当能说出它们的名字：动能、重力势能、化学能、 弹性势能、核能、静电能，以及内能或热能。
Energy is transferred between those stores in four ways: by forces doing mechanical work, by electric currents, by heating, and by waves such as light and sound.
能量在这些储存之间转移有四种方式： 靠力做机械功、靠电流、靠加热，以及靠光和声这样的波。
A roller-coaster is the classic picture.
过山车是最经典的画面。
At the top of the hill the cars have a large gravitational potential store.
在山顶时，车厢有很大的重力势能储存。
As they run down, that store empties into the kinetic store, and they speed up.
当它们冲下来时，这份储存倒进了动能储存，于是它们加速。
The principle of conservation of energy says energy is never made and never destroyed — it only moves between stores.
能量守恒定律说，能量既不会被创造也不会被消灭——它只是在各个储存之间移动。
A nought point five kilogram ball is dropped from a height of one point eight metres.
一个零点五千克的球从一点八米高处落下。
Ignoring air resistance, find its speed just before it lands, taking g as ten.
不计空气阻力，求它落地前一瞬间的速率， 取 g 为十。
All the gravitational potential energy becomes kinetic energy, so a half m v squared equals m g delta h.
全部的重力势能都变成了动能，所以二分之一 m v 平方等于 m g delta h。
Now notice something: the mass cancels from both sides.
现在注意一件事：两边的质量约掉了。
That leaves v squared equals two g delta h.
剩下 v 平方等于二 g delta h。
Two times ten times one point eight is thirty-six, and the square root of thirty-six is six point zero metres per second.
二乘以十再乘以一点八等于三十六，三十六的平方根是六点零米每秒。
And because the mass cancelled, EVERY object dropped from this height would land at the same speed — which is the whole point of the example.
而正因为质量被约掉了，从这个高度落下的每一个物体，落地时的速率都相同—— 这才是这道例题真正要说的。
Work done equals the energy transferred.
做的功等于转移的能量。
When a force moves an object, W equals F times d, and that is the same as the change in energy.
当一个力使物体移动时，W 等于 F 乘以 d， 而这与能量的变化量是同一回事。
The unit of work and of energy is the joule.
功和能量的单位都是焦耳。
Power is the work done, or the energy transferred, per unit time: P equals W over t.
功率是单位时间内做的功，或者说转移的能量：P 等于 W 除以 t。
The unit is the watt, and one watt is one joule per second.
单位是瓦特，一瓦特就是每秒一焦耳。
So a hundred-watt lamp transfers a hundred joules every second.
所以一盏一百瓦的灯每秒转移一百焦耳。
The distinction that gets tested: work is how much energy moved; power is how FAST it moved.
会被考到的区别是：功是转移了多少能量；功率是转移得有多快。
Two people carrying the same box up the same stairs do the same work — but the one who runs up has the greater power.
两个人把同一个箱子搬上同一段楼梯，做的功是一样的——但跑上去的那个人功率更大。
Efficiency tells you how much of the input energy becomes USEFUL energy: useful output divided by total input, times one hundred per cent.
效率告诉你输入的能量中有多少变成了有用的能量：有用输出除以总输入，再乘以百分之百。
A motor is supplied with two hundred joules of electrical energy and gives a load one hundred and fifty joules of gravitational potential energy.
一台电动机被输入二百焦耳的电能，给重物提供了一百五十焦耳的重力势能。
Its efficiency is a hundred and fifty over two hundred, times a hundred, which is seventy-five per cent.
它的效率是一百五十除以二百再乘以一百，等于百分之七十五。
A Sankey diagram shows this, with the band widths proportional to the energy: the two hundred joule input splits into a hundred and fifty useful and fifty wasted as heat.
桑基图把这件事画了出来，各条带子的宽度与能量成正比： 二百焦耳的输入分成了一百五十焦耳有用的，和五十焦耳作为热浪费掉的。
Efficiency is always less than a hundred per cent, because some energy is always wasted — usually as heat.
效率永远小于百分之百，因为总有一部分能量被浪费掉——通常是变成了热。
Most electricity generation works the same way: spin a turbine, which drives a generator.
大多数发电方式的原理是一样的：让涡轮转起来，带动发电机。
Fossil fuels, nuclear fuel, geothermal and biofuels all do it by boiling water to make steam.
化石燃料、核燃料、地热和生物燃料，都是靠把水烧开产生蒸汽来做这件事。
Hydroelectric, waves, tides and wind do it directly with moving water or air.
水力、波浪、潮汐和风力，则直接用流动的水或空气来做。
Solar cells are the exception — they make electricity from sunlight directly, with no turbine at all.
太阳能电池是例外——它们直接把阳光变成电，完全不用涡轮。
Those are the energy resources, and learn which are renewable: biofuels, hydroelectric, wind, solar, geothermal and tidal are; fossil fuels and nuclear are not. Solar panels heat water directly, while solar cells make electricity.
要记住哪些是可再生的：生物燃料、水力、风力、太阳能、地热和潮汐是； 化石燃料和核能不是。
And here is a fact worth knowing: almost all of these trace back to the Sun.
还有一个值得知道的事实：这些几乎全都能追溯到太阳。
Fossil fuels are ancient stored sunlight; wind and waves come from solar heating; and the Sun itself is powered by nuclear fusion.
化石燃料是远古储存下来的阳光；风和波浪来自太阳的加热。
The only exceptions are geothermal, nuclear and tidal.
唯一的例外是地热、核能和潮汐。
Energy comes in many stores — kinetic, gravitational, chemical, elastic, and more.
能量以许多形式储存——动能、重力势能、化学能、弹性势能等等。
It is never made or destroyed; it only moves from one store to another.
它从不被创造或消灭，只是从一种储存转移到另一种。
A moving object has kinetic energy — one half the mass times the speed squared.
运动的物体有动能—— 二分之一质量乘以速度的平方。
Lift it up, and it gains gravitational energy — mass times gravity times height.
把它举高，它就获得重力势能——质量乘以重力乘以高度。
So drop a ball, and its gravitational energy turns into kinetic energy.
所以让球落下，它的重力势能就变成动能。
From a height of one point eight metres, its speed just before landing is six metres per second.
从一点八米高处落下， 它着地前的速度是每秒六米。
And because the mass cancels, every object would land at the same speed.
因为质量约掉了，任何物体都会以相同的速度着地。
When a force moves an object, it does work — and the work done equals the energy transferred.
当力使物体移动时，它就做了功——做的功等于转移的能量。
Power is how fast that energy is transferred, measured in watts.
功率是能量转移的快慢，用瓦特来量。
But no machine is perfect.
但没有机器是完美的。
Some energy always escapes, usually as heat.
总有一些能量逃走，通常变成热。
Efficiency tells us how much of the energy we put in becomes useful output.
效率告诉我们，我们输入的能量有多少变成了有用的输出。
A motor given two hundred joules that delivers one hundred and fifty useful joules is seventy-five percent efficient.
一台电动机输入两百焦耳，输出一百五十焦耳有用能量，它的效率是百分之七十五。
The rest is wasted.
其余的都浪费了。
Pressure is the force spread over an area — the force divided by the area.
压强是力分布在一个面积上——就是力除以面积。
A small area gives a big pressure; that is why a sharp knife cuts so well.
面积小，压强就大； 这就是锋利的刀切得好的原因。
Inside a liquid, pressure grows with depth.
在液体内部，压强随深度增大。
The deeper you go, the more liquid there is pushing down from above.
你越往下， 上方压下来的液体就越多。
That extra pressure equals the density, times gravity, times the depth.
那份额外的压强等于密度乘以重力乘以深度。
This is why a dam is built much thicker at the bottom, where the water pushes hardest.
这就是为什么大坝在底部建得厚得多，因为那里水压最大。
Pressure is the force per unit area, p equals F over A, measured in pascals — and one pascal is one newton per square metre.
压强是单位面积上的力，p 等于 F 除以 A，单位是帕斯卡—— 而一帕斯卡就是一牛顿每平方米。
A small area gives a large pressure, which is why a sharp knife cuts.
面积小，压强就大，这正是锋利的刀能切开东西的原因。
A large area gives a small pressure, which is why snowshoes stop you sinking.
面积大，压强就小，这正是雪鞋能让你不陷进雪里的原因。
In a liquid it is different: pressure increases with depth and with the liquid's density, delta p equals rho g delta h.
在液体里情况不同：压强随深度增加，也随液体密度增加， delta p 等于 rho g delta h。
Look at the arrows — the deeper you go, the harder the liquid pushes outward.
看那些箭头——越深，液体向外推得越用力。
That is why a dam is built much thicker at the bottom.
这正是水坝底部要造得厚得多的原因。
And pressure in a liquid acts in ALL directions, not just downward.
而且液体中的压强朝各个方向作用， 不只是向下。
Find the extra pressure at a depth of two point zero metres in water, taking the density as a thousand kilograms per cubic metre and g as ten.
求水下两点零米深处增加的压强，取密度为一千千克每立方米，g 取十。
Use delta p equals rho g delta h: a thousand times ten times two point zero, which is twenty thousand pascals.
用 delta p 等于 rho g delta h：一千乘以十再乘以二点零，等于二万帕斯卡。
Now the trap, and it is worth stating clearly: there are two pressure formulas and they are for different situations.
现在说那个陷阱，而且值得说清楚：压强有两个公式，它们用于不同的情形。
Use p equals F over A for a solid pressing on a surface.
固体压在表面上，用 p 等于 F 除以 A。
Use p equals rho g h for the pressure INSIDE a liquid.
液体内部的压强，用 p 等于 rho g h。
Choosing the wrong one is a common way to lose the mark, so ask yourself first: is this a solid pushing, or a depth in a fluid?
选错公式是常见的丢分方式，所以先问问自己：这是固体在压，还是流体中的深度？
Before you go, three marks students often lose.
结束之前，三个学生常失的分。
First, on a distance–time graph the gradient is the speed, but on a speed–time graph the gradient is the acceleration, and the area is the distance.
第一，在距离–时间图上斜率是速率， 但在速度–时间图上斜率是加速度，而面积是距离。
Never mix them up.
千万别搞混。
Second, mass and weight are not the same — mass is in kilograms, weight is a force in newtons: mass times the gravitational field strength, about ten newtons per kilogram on Earth.
第二，质量和重力不一样——质量用千克，重力是力，用牛顿。
Third, always convert your units first: centimetres to metres, grams to kilograms, before you put numbers into a formula.
第三，先换算单位：厘米换成米，克换成千克，再把数字代入公式。
Get these right, and this topic is yours.
把这些做对，这个专题就是你的了。