1. Imagine 50 black and 50 white soccer balls lined up alternatingly on the cent

Question

1. Imagine 50 black and 50 white soccer balls lined up alternatingly on the center line of a soccer field. A player shoots one ball after another towards the goal line. Assume the player does not get tired and kicks each ball approximately with the same energy. When he/she is done you count w = 12 white balls and b = 8 black balls that made it beyond the goal line.

a) Which balls do you think are heavier? Why do you think that? (2)


b) Let’s define the ratio R = b/(b+w) as the number of black balls divided by the number of total balls. Since we have the same amount of black and white balls initially, a convenient standard would be Rstd = 1/2. Calculate the delta values d = (R/Rstd) – 1 for the initial set-up on the center line, and for the balls that made it behind the goal line. (3)


Now imagine the same experiment but starting with 20 black and 80 white balls at the center line. Their weight difference is the same as before. Another player kicks the balls again towards the goal line. This player shoots a total of 25 balls behind the goal line.  

c) Do you expect a larger or smaller number of black balls behind the goal line than in (b)? Why? (2)


d) How many black and white balls do you expect to find behind the goal line? Tip: for your standard now choose Rstd = 20/100 to reflect the different number of balls to begin with and use the delta value from (b) to calculate R. (3)


e) For real isotopes the ratios are much smaller. E.g. the abundance of oxygen-18 is only 0.2% compared with oxygen-16, for which it is 99.8%. These numbers reflect sea water, on which the standard ratio Rstd is based. Calculate Rstd for ocean water. (1)


f) Water ice in ice sheets has a delta value of about d = -40 permil. Calculate its isotopic ratio with respect to Rstd of sea water. (Remember that permil means per thousand.) (2)

Explanation / Answer

1 Initially there were equal white and black balls in the field and after the player shoots all the balls we find that number of black balls that goes beyond the goal post is less hence we can say that black balls are heavy as compared to white balls.

b) d for initial setup = (1/2)-1= 1/2

d (for the balls that made beyond the goal line) = (12+8)/(50+50) = 20/100 = 0.2

c) The number of white ball will be more as the increase in white balls’ number is very high while the number of black balls decreased a lot.

d) The number of white ball beyond goal = (12/50) x 80 = 19.2 or 20

Number of black ball beyond goal = (8/50) x 20 = 3.2 or 4

As per Chegg’s policy we are advised to attempt first 4 parts of questioner, please post the remaining questions as a different questioner. Thanks

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