To navigate
choose an item below Puzzled person
Overview News Lectures Problems

Problems

Problem-solving is a skill you have to learn, as opposed to one you can be taught, and the only way to learn it is to practise. You should aim to do all the examples on both the example sheets, whether they are set as assessed homework or not. Note that I stole all the examples in Sheet 1 from an exam which allows 15 minutes per question. They aren't all equally difficult, so some of them may genuinely take more than 15 minutes, but if you are still stuck after half an hour you need to ask for help!

Click on the titles below to download each problems sheet as a pdf file. Click here to jump down to sheet 2.

Example Sheet 1

These are general examples using a range of physical principles. All the equations you need are on the Toolkit sheet. To see a couple of examples of how to apply our four-step strategy to problems like these, look at pages 9-15 of Lecture 1.

Some basic hints, applicable to all questions

Example Sheet 2

Most of these are exercises in dimensional analysis. There are several examples in Lecture 2. Note that you can apply dimensional analysis to a problem even when you have only a very hazy idea of the underlying physics.

Scaling problems are closely related to dimensional analysis problems. If you have concluded that yx2, then if you double x you multiply y by 4, regardless of the actual values of x and y.

Simple example of a scaling problem

Five men take five days to dig five holes in the road. How many holes can two men dig in two days?
It's very tempting to say "two", isn't it? But think of scaling:
  1. Obviously, the number of holes that can be dug is proportional to the number of men doing the digging – 10 men could dig 10 holes in five days.
  2. The number of holes that can be dug is also proportional to the time spent digging: if the five men spend another five days they can dig another five holes, so five men can dig 10 holes in 10 days.
  3. Therefore, using (1), one man takes five days to dig one hole. Using (2), one man digs 1/5 of a hole in one day (presumably this means a hole the same size, but only 1/5 as deep!).
Therefore, two men in two days can dig 2x2x1/5 = 4/5 of a hole.

Hints for dimensional analysis problems