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Which Twin Is Older?

A simplified account of special relativity and the twins paradox.

Snookered

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Spokes

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

Smoke and Daggers

Age 16 to 18
Challenge Level

Hint
Each compound contributes to the total pressure in her lungs, known as the partial pressure. Can you work out the partial pressure that each of the compounds contributes?

Make sure you consider the moles of "air" molecules present in Ellie's lungs which also contribute to the partial pressure.

Hint
What is the density of the cigarette smoke containing air in her lungs?

Make sure you take into account the masses of the components of alveolar air as well as the unusual components of the smoke given already.

Hint
What is the average concentration of nicotine in Ellie's blood given that systolic blood pressure is 120 mmHg, the diastolic blood pressure is 80 mmHg?

An equation is required that links pressure and volume as well as number of moles. Also consider the value of blood pressure compared to atmospheric pressure. The conversion from mmHg to Pa has been provided earlier in the question.

Hint
How long does it take for levels of nicotine to drop below the 200 ng/ml detectable level so that Ellie can cheat her test?

Nicotine uptake into the blood stream is rapid compared with its half-life. This can be seen by doing a rough calculation. You might approximate the uptake to be instantaneous in your calculation.

Hint
Assuming that none of these dangerous compounds is absorbed into the blood stream over this period, what is the percentage of dangerous compounds in the alveolar air for Ellie and her brother, Pete, after the last outward breath?

Consider how the percentage of dangerous compounds varies with the first few inward and outward breaths. Can you see any patterns?