A very busy day today so I thought I’d wind down by giving you a chance to test your brains with some order-of-magnitude physics problems. I like using these in classes because they get people thinking about the physics behind problems without getting too bogged down in or turned off by complicated mathematics. I’ve also kept some of these in archaic units just to annoy people who can only do things in the SI system. I think it’s good to practice swapping between systems, especially for us astro-types who use all kinds of bizarre units, so if you don’t know the units, look them up! And if there’s any information missing that you need to solve the problem, make an order-of-magnitude estimate!
Give order of magnitude answers to the following questions:
- What is the mass of a body whose weight is equivalent to the total force exerted by a 40 mph gale on the side of a house 40 ft long and 20 ft high? Express your answer in tons.
- What is the power required to keep in the air a helicopter of mass 500 kg whose blades are 3m long? Express your answer in kilowatts.
- The base of the Great Pyramid is 750 ft square and its height is 500ft. How much work was done building it? Express your answer in Joules.
- How high would the jet of a fountain reach if it were aimed vertically up and supplied by a water main in which the pressure is 3 atmospheres? Express your answer in feet.
There’s no prize involved, but feel free to post answers through the comments box. It would be helpful if you explained a bit about how you arrived at your answer!