For a chance to win the first prize (£100 Amazon voucher), or one of our prizes for runners-up, submit your typed or neatly written solutions of the following problems to firstname.lastname@example.org or by post to Physics Challenge, School of Mathematics and Physics, University of Lincoln, Lincoln, LN6 7TS. Please include your full name, postal address and email, as well as the name and address of your school. The closing date is 5 January, 2017. The competition is open to all young pre-university people in UK aged 16–18 years. It is not open to current university students. See full Terms and Conditions. The problems can also be downloaded from here.
1. A log of radius R rolls towards a frog with speed v. What is the minimum upwards velocity u with which the frog has to jump in order to jump over the log? How close can the log get before the frog must begin to jump?
2. The Brayford Pool in Lincoln is on average 5 metres deep and it’s approximate shape is drawn below:
Estimate what the outside temperature would need to be in order for the pool to entirely freeze within three months during a very cold winter (assume the initial temperature of the water is 0°C).
3. A double pendulum is often called a ‘chaotic pendulum’. Why is this the case? What are the Newtonian equations of motion for the system?
4. Medieval stained glass windows such as the famous ‘Dean’s Eye’ of Lincoln Cathedral were typically stained using metallic compounds or tiny metal crystals. Despite the artists not having any idea about the physics involved, the results were spectacular (picture courtesy of www.geograph.co.uk)!
Explain why different metal compounds and crystals produce different colours when incorporated into glass, using any equations or diagrams that may help to illustrate your answer.
5. According to historical accounts, when the Saxons were debating an issue they would take it in turns to speak for a limited amount of time. To regulate this procedure, at the beginning of a speaker’s argument they would start a primitive clock. A bowl, which had a small hole made in its base, would be placed onto the surface of a larger bowl containing water; the smaller bowl would sink slowly as water rushed in through the bottom, and when it was completely submerged the speaker’s time was over.
Design and carry out an experiment to determine how the size of a hole in the bottom of a container influences the time taken for it to become completely submerged in a ‘bath’ of water.
Note: A winning submission may not necessarily be based on all five problems – you are encouraged to submit solutions even if you only do some of the problems.