Warning - Science Content!!!

[mcauleyab]

Well, as promised, here is my next attempt at a competition. Rather than trying to find new and original logic problems/trivia questions etc., I thought a set of wierd science (mostly) problems would be an interesting change. (And, as a scientist, I felt there wasn't enough science content here either )

So I am offering 200 credits for the first correct answer to each of the following problems (working/ calculations/ explanations are required too). So get your calculators out and get cracking! I will increase the prize too every few days if no-one has solved them.

1. Suppose Muppet Labs discovers a new radioactive element "Bunsonium" with a half-life of 7.3 years. Any sample greater than 12 grams of Bunsonium emits harmful radiation. On his way to the storage shelter, poor old Beaker trips and manages to spill exactly 5 kg of Bunsonium. How long does Beaker stay contaminated for (i.e. when the amount of active material has reduced to 12g) ? (solved)

2. Now let us assume that we have a little bubble of air somewhere in the sea. If the pressure under the sea increases by 1 atmosphere every 10 metres in depth, at what depth would this little bubble "sink"? (Assume that the pressure on the bubble is entirely due to water pressure, and that air is 75% Nitrogen and 25% Oxygen)

3. Most of us would not feel uncomfortable sitting in a room with a temperature of 15 degrees Celsius. However, this is a full 22 degrees below the temperature of our bodies. So....why don't we feel cold? (Admittedly this is a simplification. The true physiological processes involved are complex, and some people ARE cold!)

4. Suppose you have a bagpiper standing on top of a tall tower. He starts to play, just one continuous note in the key of E4 (E above Middle C). Not liking bagpipers, and especially ones with nothing better to do than play on the rooftop this early in the morning, you push him off the roof. Being a dedicated bagpiper, however, he continues to play this one note all the way down. Your friend, who lives at the bottom of the tower, notices that as the bagpiper passed his window, the note changed in pitch to Middle C. Given that the frequency of E4 is 329.628 Hz, and ignoring air resistance, calculate how fast the bagpiper was falling as he passed your friend's window, and therefore, what is the distance between the tower roof and your friend's window?

5. Suppose an asteroid with a mass of 1 million tons is discovered orbitting the earth at a distance of 2 million km. What is the gravitational attraction between the earth and the asteroid? (solved)

6. Now as it turns out, the asteroid in Q5 is not really an asteroid. It is actually a perfectly spherical metal ball. (Don't ask how it got there - work with me here) If the ball has a diameter of 62.42m, which pure metal is it made of given the following densities?
Water = 1.0 Zinc = 7.135 Iron = 7.85 Copper = 8.93 Gold = 19.32
(solved)

7. More fun with gravity. You've been transported via a black hole to an alternate universe, where you find yourself suspended in a void with nothing but a ping-pong ball for company. You weigh 100kg, the ball weighs 2g and you are 20m apart. How long will the ball take to reach you through nothing but gravitational attraction? (Assuming that you stay still and the ball moves to you, and that the gravitational constant in this alternate universe just happens to be the same as in the original)

8. Having made it back to your own universe, you know find yourself with another problem. You need to make a flask of tea, but all you have is a 1kg block of ice at -20 degrees Celsius and a 100W lightbulb. How long does it take to turn the ice entirely into water at a temperature of 99 degrees Celsius using only the lightbulb? (asuming that all of the energy from the lightbulb is converted to heat, and that the heat from the lightbulb is the only thing heating the ice)

Hopefully this proves of some amusement. If anyone needs hints/constants etc, just ask and I'll see what I can do. Oh, and in case anyone was worried, the bagpiper landed in the back of a foam rubber truck that just happened to be passing. Lucky that.

[TheGuru]

With Question 7 you are talking about mass and not weight arent you :?: I'm sure that they are different :-k

Great questions ;-)

[salocius]

Think I've done 1,5 and 6.

Still working on the rest :-k

[madcat]

Wow - they are good questions.. above my science knowledge though I think!!

MadCat

[mcauleyab]

Originally Posted by TheGuru

With Question 7 you are talking about mass and not weight arent you :?: I'm sure that they are different :-k

Quite correct! I really should have worded it "You have a mass of 100kg" as the weight is indeed unknown.

[TheGuru]

Originally Posted by mcauleyab

Quite correct! I really should have worded it "You have a mass of 100kg" as the weight is indeed unknown.

I just need to work out the answer now

:-k ](*,) 8-[

[mrmojorisin]

What is middle C frequency? I dont think the bagpiper problem can be solved without this info.

Cheers
M

[salocius]

I agree with you. I think you need to know the pitch drop to ascertain the speed of the piper :!:

Middle C is 261.6 Hz ;-)

[salocius]

In question 4 you can't calculate the height of the tower from the information given. You can only calculate the distance from the top of the tower to the window (unless the window is at ground level which it can't be if the piper fell past it!) :-?

[mcauleyab]

Originally Posted by salocius

I agree with you. I think you need to know the pitch drop to ascertain the speed of the piper :!:

Middle C is 261.6 Hz ;-)

I deliberately left that information out, for you to find out on your own, but yes, 261.6Hz is correct. In a few of the questions, a piece of information has been left out, such as a constant or a necessary equation. However, they are all easily located, and justs adds to the challenge!