I牛津官方（6）
"How would you design a gravity dam for holding back water?"
先建力模型（水压随深度线性增加、合力在距底 1/3 处），再谈抗倾覆与抗滑动。
"Place a 30cm ruler on top of one finger from each hand so that you have one finger at each end of the ruler, and the ruler is resting on your fingertips. What happens when you bring your fingers together?"
预设会倒，实际同时到达中心——摩擦力随正压力变化导致的交替滑动。
"Sketch the velocity of the ball as a function of time, from start to when it hits the ground."
图像题官方样题；面试官点评：更在意严谨思考而非正确答案。
"Sketch the graph of y = sin x / x. Differentiate the original function. Square the original function. Sketch the graph of this squared function. Is this pattern familiar?"
官方解答要点：两函数逐点相乘 → x→0 时 y→1 → x=nπ 处为零 → 振幅随 1/x 衰减 → 偶函数对称 → 平方后即单缝衍射图样。
"An object of mass 25 kg and density 50 kg/m⁻³ is tethered to the bottom of a tank of water by a string. What is the tension in the string?"
浮力大于自重，绳向下拉；关键是用「排开水的重量」而不是物体自身重量。
"How high up a mountain could I go having eaten a banana?"
E=mgh 估算；m≈60 kg、g≈10；再讨论人体效率与非竖直爬升的损耗。
II剑桥工程系官方题库（3）
"A small object of mass 10 kg is suspended by three light inextensible strings which are fixed at the points (0,0,4), (3,3,4) and (0,6,4) … Each of the strings is of length 4 units. What is the highest tension in any of the three strings?"
三维力平衡 + 几何陷阱：悬挂点水平位置是三角形外心，其中一根绳张力为零。
"A weight of mass m is suspended by a light string of length l from the ceiling. It swings in a horizontal circle such that the string describes the outline of a cone … Calculate the period of the conical pendulum, T."
"For a conventional clock, how many times does the minute hand make a right angle with the hour hand in one day?"
相对角速度 330°/h；一天相对转 22 圈、每圈 2 次 ⇒ 44 次。
III剑桥工程回忆题（30）
Draw a ladder leaning against a wall and mark every force that acts on it. Where does each force come from?
Which footing keeps a bridge steadier — one cast in concrete or one set in soil? Explain the reasoning.
What actually protects a building during an earthquake? Walk through the mechanisms.
Suppose someone asked you to span the Atlantic with a bridge. What would stop you, and where would you start?
A closed cylinder is pressurised from inside. Do you expect the ends to pop off first, or the curved wall to split along its length? Why?
Old mill chimneys were built unusually tall. What was the point of the height?
An aircraft carrier weighs tens of thousands of tonnes yet floats. Account for that.
When we treat a flow as potential flow, what are we assuming, and what do we give up?
Explain how a wing generates lift. Can the same account explain inverted flight?
What keeps an airliner in the air, and why can some aircraft fly upside down without falling out of the sky?
Sausages tend to burst along their length rather than around the middle. Why?
A windmill's blades often look frozen or slowly drifting on video. What is happening?
Name the hardest naturally occurring material, and explain how it can be worked or cut.
A circular hole is cut in a metal plate, and the plate is then heated. Does the hole grow, shrink, or stay the same?
Starting from the definition, derive the relation between charge, voltage and capacitance.
What makes superconductors interesting, and where would you use one?
State Moore's law, then explain what physically limits how small a chip can get.
How far can you shrink a computer? List the constraints, from the transistor up to the package.
Start with a rectangle a by b. Cut equal squares of side h from each corner, fold up the sides. What h gives the largest open box?
Differentiate sin x + cos x + tan x with respect to x.
Derive the area of a circle without quoting the formula.
Six people are in a room and you guess each birthday at random. What is the chance that exactly one guess is right?
Contrast the engines of a fighter jet and a passenger jet. Why are they built so differently?
What separates a rifle from a smooth-bore gun, and what does spin do for the projectile?
Where does engineering stop and physics begin? Give your own view.
Explain force, work, power and momentum to someone who has never studied physics.
If you could invent one thing, what would it be and why?
Draw the speed of a skydiver against time, from the jump to well after the parachute opens.
Imagine a tunnel bored straight through the Earth. You step in and let go. Describe what happens.
Tell me everything worth knowing about a light bulb.
IV剑桥自然科学回忆题（9）
An ice cube floats in a glass of water and then melts. What happens to the water level?
A tennis ball sits on top of a basketball; the pair is dropped together. How high does the tennis ball rebound?
Using only the energy in one chocolate bar, how far up a mountain could you climb?
Mars 条爬山 · 能量估算（牛津官方版是香蕉）
A shaft is dug all the way through the Earth and you jump in. What kind of motion do you experience?
A fridge runs with its door open inside a sealed, insulated room. What happens to the room's temperature?
How many times would you have to fold a sheet of paper in half for the stack to reach the Moon?
Sketch how a skydiver's displacement and velocity vary with time after jumping.
Why does a candle refuse to burn inside a spacecraft?
Two identical beakers with equal amounts of water sit on a balance. A steel ball hanging from a string is lowered into one of them without touching the bottom. Does the balance tip?