Warning - Science Content!!!

[mcauleyab]

Originally Posted by 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!) :-?

Again, you are completely correct, as the piper has to fall past the window in order for the friend to experience the change in pitch. However, I did say to assume that the friend was at the bottom of the tower, to simplify matters. So I'll reword the question to be, "What is the distance from the top of the tower to your friend's window?" ;-)

[mcauleyab]

Ok. Interest appears to be waning in this quiz, so I'll kick it up a notch. I'll change the competition rules so that you can answer one question at a time, instead of having to get all of them. And I'll change the prize to be 200 credits per question for a grand total of 1600 credits. :shock: ;-)

[salocius]

Right OK. Here goes...

1) The half-life is the time it takes for the radioactive material to decay to half its level.
So, after 7.3 years the material will have decayed to 2500g
14.6 yrs = 1250g
21.9 yrs = 625g
29.2 yrs = 312.5g
36.5 yrs = 156.25g
43.8 yrs = 78.125g
51.1 yrs = 39.0625g
58.4 yrs = 19.53125g
65.7 yrs = 9.765625g

We want the time at which it reachs 12 grams, so it is between 58.4 yrs and 65.7 yrs.
By calculation, assuming a constant rate of decay:
((19.53125-12)/(19.53125-9.765625))*7.3 = 5.6

Therefore time at which material reaches 12g is 58.4+5.6 = 64 years.

[salocius]

3) The reason we don't feel cold in a room at 15°C is because a stable layer of air forms around our body and quickly heats to the body temperature. As soon as a draft or wind is introduced the air is constantly moving and we feel the actual temperature of the air (feel cold)

[salocius]

6) Right, volume of a sphere (v) = (4/3)*PI*r³

The diameter of the asteroid is 62.42m so r = 31.21m

So, v = (4/3)*PI*31.21³ = 127341.5m³

Mass of asteroid = 1 million tons

density = mass/volume = 1000000000Kg/127341.5m³ = 7852.9 Kg/m³

The asteroid must be made of Iron, having a density of 7.85 Mg/m³ or 7850 Kg/m³

[salocius]

5) Gravitational attraction = (G*m1*m2)/d²

where, G = constant of proportionallity = 6.67*10(-11)Nm²/Kg²

m1 is mass of the earth = 5.98*10(24)Kg
m2 is the mass of the asteroid = 1*10(9)Kg

d is the distance between objects

so, ((6.67*10(-11))*(5.98*10(24))*(1*10(9)))/(2*10(9))²

= 99716.5 N
or 99.7 kN

[mcauleyab]

Salocius - your answers to Questions 5 and 6 are spot on, so that's 400 credits coming your way.

With Question 1, your answer is very close, but you've used the Brute Force method to get there, rather than proper mathematical technique. (Sorry! )

Similarly, with Question 3 you're definately getting close. Your answer is half right.

[salocius]

Here's no 1 again.

half-life = (elapsed time x log2)/(log(beginning value/end value))

So by rearranging for time,

elapsed time = (7.3(log(5000/12)))/log2

Therefore elapsed time = 63.53 years

[mcauleyab]

Originally Posted by salocius

Here's no 1 again.

half-life = (elapsed time x log2)/(log(beginning value/end value))

So by rearranging for time,

elapsed time = (7.3(log(5000/12)))/log2

Therefore elapsed time = 63.53 years

Yes, that's it precisely. 200 more credits on their way!

[mcauleyab]

As per my promise, and in the spirit of post-Christmas sales, I am once again upping the prize to a crazy 250 tokens per correct, justified answer. :-o There are still 5 unanswered questions, so that's a potential 1250 tokens up for grabs. Don't forget, just ask if you need any hints/clues for any of the questions.