Archive for the Cute Problems Category

Yet another easy physics problem…

Posted in Cute Problems with tags , , , on December 2, 2019 by telescoper

Last week I posted a little physics problem that generated a large amount of traffic (at least by the standards of this blog), so I thought I’d try another one.

The examination comprised two papers in those days (and a practical exam); one paper had long questions, similar to the questions we set in university examinations these days, and the other consisted of short questions in a multiple-choice format. This question is one of the latter. Incientally, for those of you who have asked, the multiple-choice examination contained 50 such questions to be answered in 2½ hours, which is three minutes per question.

(You can assume that the acceleration due to gravity is 9.8 ms-2.)

And here is a poll in which you may select your answer:

Comments on or criticisms of the question are welcome through the comments box…

Another easy physics problem…

Posted in Cute Problems, The Universe and Stuff with tags , , , on November 26, 2019 by telescoper

Many moons ago I posted an `easy’ physics problem from the Physics A-level paper I took in 1981. The examination comprised two papers in those days (and a practical exam); one paper had long questions, similar to the questions we set in university examinations these days, and the other consisted of short questions in a multiple-choice format. The question I posted was one of the latter type. I was reminded about it recently because, years on, it appears people are still trying it (and getting it wrong).

Anyway, since I’m teaching similar things to my first-year Mathematical Physics class I thought I’d put up another question from the same paper.

And here is a poll in which you may select your answer:

Comments on or criticisms of the question are welcome through the comments box…

 

 

 

The Problem of the Disintegrating Asteroid

Posted in Cute Problems, The Universe and Stuff with tags , , on September 30, 2019 by telescoper

I thought you might enjoy this entry in the Cute Problems folder.

An asteroid is moving on a circular orbit around the Sun with an orbital radius of 3AU when it spontaneously splits into two fragments, which initially move apart along the direction of the original orbit. One fragment has a speed which is a fraction 0.65 of the original speed, the other has a speed of 1.35 times the original speed. The original orbit (solid line) is shown above, along with the two new orbits (dashed and dotted).

  1. Which orbit does the fast fragment follow, and which the slow fragment?
  2.  Calculate the original orbital speed in AU/year.
  3. Calculate the angular momentum per unit mass, h, of the original asteroid and of each of the two fragments in units of AU2 per year. [HINT: Show that in these units, for a general orbit of eccentricity e and semi-major axis a, h2=4π2 a (1-e2).]
  4.  Calculate the eccentricities of the orbits of the two fragments.
  5.  Calculate the orbital periods of the two fragments in years.

Answers please through the Comments box. First complete set of answers wins a trip to the Moon on gossamer wings.

 

 

A Problem of Dimensions

Posted in Cute Problems, Maynooth, The Universe and Stuff with tags , , , on August 21, 2019 by telescoper

We’ve more-or-less sorted out who will be teaching what next term in the Department of Theoretical Physics at Maynooth University next term (starting a month from now) and I’ll be taking over the Mathematical Physics module MP110, which is basically about Mechanics with a bit of of special relativity thrown in for fun. Being in the first semester of the first year, these is the first module in Theoretical Physics students get to take here at Maynooth so it’s quite a responsibility but I’m very much looking forward to it.

I am planning to start the lectures with some things about units and dimensional analysis. Thinking about this reminded me that I posted a dimensional analysis problem (too hard for first-year students) on here a while ago which seemed to pose a challenge so I thought I would post another here for your amusement.

 

The period P for an elliptical orbit of semi-major axis a of  a moon of mass m around a planet of mass M, depends only on the quantities  a, m, M and G (Newton’s Gravitational Constant).

(a). Using dimensional analysis only, determine as completely as possible the relationship between P and these four quantities.

(b). How would the period P compare with the period P′ of a system consisting of a moon of mass 2m orbiting a planet of mass 2M in an ellipse with the same semi-major axis a?

Please submit your efforts through the comments box below.

 

More Order-of-Magnitude Physics

Posted in Cute Problems with tags , , , on April 25, 2019 by telescoper

A very busy day today so I thought I’d just do a quick post to give you a chance to test your brains with some more 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. 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:

  1. What is the maximum distance at which it could be possible for a car’s headlights to be resolved by the human eye?
  2. How much would a pendulum clock gain or lose (say which) in a week if moved from a warm room into a cold basement?
  3. What area would be needed for a terrestrial solar power station capable of producing 1GW of power?
  4. What mass of cold water could be brought to the boil using the energy dissipated when a motor car is brought to rest from 100 km/h?
  5. How many visible photons are emitted by a 100W light bulb during its lifetime?

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!

A Problem of Sons

Posted in Cute Problems with tags , , on January 31, 2019 by telescoper

I’m posting this in the Cute Problems folder, but I’m mainly putting it up here as a sort of experiment. This little puzzle was posted on Twitter by someone I follow and it got a huge number of responses (>25,000). I was fascinated by the replies, and I’m really interested to see whether the distribution of responses from readers of this blog is different.

Anyway, here it is, exactly as posted on Twitter:

Assume there is a 50:50 chance of any child being male or female.

Now assume four generations, all other things being equal.

What are the odds of a son being a son of a son of a son?

Please choose an answer from those below:

 

UPDATE: The answer is below:

 

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Acute Geometry Problem

Posted in Cute Problems, mathematics on December 3, 2018 by telescoper

I saw a plea for help on Twitter from Astronomer Bryan Gaensler who is stuck with his son’s homework.

So please give him a hand by solving this to find a, b and c.

Your time starts now.