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QUIZ 7 Physics 101, Fall 2005Throughout, please box your answers!

Problem 1. A cylindrical candle floats in a measuring cup full of water with density 1gm/cm3. It is made of volume 100 cm3 of wax with density 0.2 gm/cm3 and has a lead pelletof mass 5 gm and negligible volume embedded in its bottom which makes it float uprightand causes it to extinguish itself automatically.

Water

Pellet

Starting point End point

Water

a. (2 pts) What volume of water does the candle displace before it is lit (fig./left)?

Vwaxρwax + mp = ρH2OVH2O

Solve for VH2O = [Vwaxρwax + mp]/[ρH2O] = [100 cm3 x 0.2 gm/cm3 + 5 gm]/[1 gm/cm3] =25 cm3

b. (2 pts) The candle burns without dripping into the water, so it reduces to a shorter lengthby evaporating mass (wax) until the water reaches the wick when it is barely submerged .What is the final volume of leftover candle (fig./right)?

Vleftover−candleρwax + mp = ρH2OVleftover−candle

Solve for Vleftover−candle = [mp]/[ρH2O - ρwax] = [5 gm]/[1 gm/cm3 - 0.2 gm/cm3] = 6.25 cm3

c. (1 pts) Has the water level in the measuring cup gone up or down ? Justify your answer.

Goes down because Vleftover−candle - VH2O < 0

QUIZ 7 Physics 101

Problem 2. Blood Flow(1) (2 pts) The mean (gauge) pressure in an artery near the heart is 13.3 kPa (Kilo-Pascal).Your head is about 0.4 m above your heart. Neglecting the viscosity of blood and changesin the cross-sectional areas of the arteries, calculate the mean (gauge) pressure in arteriesnear your brain. (Assume that the density of blood is the same as that of water).

P1 + ρgh1 = P2 + ρgh2

where, h2 -h1 = 0.4 m

P2 = P1 - ρg (h2 -h1)

= 13300 Pa - (1000 kg/m3)(9.8 m/s2)(0.4 m) = 9400 Pa

(2) (3 pts) The aorta has an inner radius of approximately 0.25 cm. The average speed ofblood through the aorta is 1 m/s. A capillary has an inner radius of approximately 0.005 mmand the average speed of blood through a capillary is 1 cm/s. Assuming that all the bloodflowing through the aorta flows through the capillaries determine the number of capillariesin the circulatory system.

Volume flow rate is constant.

Aaortax vaorta = Ncapillaries x Acapillary x vcapillary

Ncapillaries = [Aaortax vaorta]/[Acapillary x vcapillary] = [π (raorta)2 x vaorta]/[π (rcapillary)2 x

vcapillary] = [(0.25x10−2 m)2 x 1 m/s)]/ [(5x10−6 m)2x 0.01 m/s] = 2.5x107

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