Simple Nature - Light and Matter

41 Estimate the number of man-hours required for building theGreat Wall of China. ⊲ Solution, p. 93242 (a) Using the microscope photo in the figure, estimate themass of a one cell of the E. coli bacterium, which is one of themost common ones in the human intestine. Note the scale at thelower right corner, which is 1 µm. Each of the tubular objects inthe column is one cell. (b) The feces in the human intestine aremostly bacteria (some dead, some alive), of which E. coli is a largeand typical component. Estimate the number of bacteria in yourintestines, and compare with the number of human cells in yourbody, which is believed to be roughly on the order of 10 13 . (c)Interpreting your result from part b, what does this tell you aboutthe size of a typical human cell compared to the size of a typicalbacterial cell?43 The figure shows a practical, simple experiment for determiningg to high precision. Two steel balls are suspended from electromagnets,and are released simultaneously when the electric currentis shut off. They fall through unequal heights ∆x 1 and ∆x 2 . Acomputer records the sounds through a microphone as first one balland then the other strikes the floor. From this recording, we canaccurately determine the quantity T defined as T = ∆t 2 − ∆t 1 , i.e.,the time lag between the first and second impacts. Note that sincethe balls do not make any sound when they are released, we haveno way of measuring the individual times ∆t 2 and ∆t 1 .(a) Find an equation for g in terms of the measured quantities T ,√∆x 1 and ∆x 2 .(b) Check the units of your equation.(c) Check that your equation gives the correct result in the casewhere ∆x 1 is very close to zero. However, is this case realistic?(d) What happens when ∆x 1 = ∆x 2 ? Discuss this both mathematicallyand physically.44 Estimate the number of jellybeans in figure o on p. 44.⊲ Solution, p. 932Problem 42.Problem 43.Key to symbols:easy typical challenging difficult very difficult√An answer check is available at www.lightandmatter.com.Problems 53