Problem 2: (6 points) Although these quantities vary, assume that a cell is a sp

Question

Problem 2: (6 points) Although these quantities vary, assume that a cell is a sphere of 2.0 m in diameter. Assume the weight of a person to be 72 kg and that cells fill the person completely. (a) How many cells are in a person? (NS) (b) What is the average mass of one cell in g. (NS) Problem 3: (6 points) A typical human contains about 5.0 liters of blood and it takes 55 s for all of it to pass through the heart once when the person is resting with a pulse of 70 heartbeats per minute. On average, what volume of blood does the heart pump during each beat? (a) Express your answer in liters. (NS) (b) Express your answer in cm. (NS) Problem 4: (5 points) Baseball rules specify that a regulation ball shall weigh no less than 5.00 ounces and no more than 5 ¼ ounces. (1 oz. = 28.35 g) (a) What are the acceptable limits, in grams for a regulation ball? (NS) Problem 5: (6 points) Based only on consistency of units, determine whether the following formulas could be correct? In each case A is the area, V the volume, R the radius, and C the circumference (a) A = 2nR (compare units) (b) V-4/3 TR' (compare units) (c) A = 2nR2 (compare units) (d) V = 6nR3 (compare units) (e) C-2nR2 (compare units) (f) V = C 'A (compare units)

Explanation / Answer

5A.

A = 2*pi*R

SI Unit of A = Area = [L]2

SI unit of pi = dimensionless

SI unit of 2 = dimensionless

SI unit of R = [L]

for the formula to be dimensionally correct

dimension of A = dimension of 2*pi*R

[L]2 = [L]

Since above is not true, So it's INCORRECT.

B.

V = (4/3)*pi*R^2

dimension of V = [L]3

dimension of R = [L]

[L]3 = ([L])2

Again it's INCORRECT

C.

A = 2*pi*R^2

Using dimension of A and R

[L]2 = ([L])2

Above expression is CORRECT

D.

V = 6*pi*R^3

Using dimension of V and R

[L]3 = ([L])3

Above expression is CORRECT.

E.

C = 2*pi*R^2

dimension of C = circumference = m = [L]

So,

[L] = ([L])2

Above expression is INCORRECT

F.

V = C*A

using known dimensions

[L]3 = [L].[L]2 = [L]1+2 = [L]3

So expression is CORRECT.

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