Question 1

According to Fick's Law, which of the following changes would most effectively increase the rate of oxygen diffusion into a cell, assuming all other variables are held constant?

Accepted Answer

Increasing the diffusion coefficient $$D$$

Question 2

A spherical cell must balance the rate of oxygen arrival with the rate of oxygen consumption to avoid suffocation. If the metabolic consumption rate $$M$$ doubles, what happens to the maximum possible cell radius $$R$$?

Accepted Answer

$$R$$ decreases by a factor of $$\sqrt{2}$$

Question 3

Which of the following best explains why most animal cells are smaller than 100 $$\mum in $$diameter?

Accepted Answer

Diffusion of oxygen becomes insufficient for metabolic needs in larger cells

Question 4

Given the following values: $$D = 2 \cdot 10$$^{-9}$$ m^2$/s, c_0$ = 10 mg/L$$, $$ho = 1 g/cm$^3$$, $$M = \frac{30\,	ext{L}}{1\,	ext{min} \cdot 75\,	ext{kg}}$$, use the formula $$R = \sqrt{\frac{3 D c_0$}{ho M}} to $$estimate the order of magnitude of the maximum cell radius $$R in $$meters.

Accepted Answer

$$10^{-4} m$$

Question 5

Which of the following cell types has the largest average volume according to the provided data?

Accepted Answer

Oocyte

Question 6

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates with no friction. What is the angular frequency $$\omega of $$the motion?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 7

If the amplitude $$A of a $$simple harmonic oscillator is doubled, what happens to the period $$T of $$the oscillation?

Accepted Answer

The period remains unchanged

Question 8

A 100 g mass stretches a spring from 10 cm to 12 cm. What will be the length of the spring if a 200 g mass is used instead?

Accepted Answer

14 cm

Question 9

Which of the following best describes the velocity and force on a mass at the equilibrium position during simple harmonic motion?

Accepted Answer

Velocity is maximum, force is zero

Question 10

A cell is modeled as a sphere. If its radius is doubled, by what factor does its volume increase?

Accepted Answer

8

Question 11

Which of the following statements about the graphs of position, velocity, and acceleration for simple harmonic motion is correct?

Accepted Answer

Acceleration is always opposite in sign to position

Question 12

Which of the following is the correct expression for the velocity as a function of time for a mass-spring system undergoing simple harmonic motion with amplitude $$A$$ and angular frequency $$\omega$$?

Accepted Answer

$$v(t) = -A \omega \sin(\omega t)$$

Question 13

Which of the following best explains why friction is often neglected in introductory discussions of simple harmonic motion?

Accepted Answer

Neglecting friction simplifies the analysis and reveals the fundamental properties of oscillatory motion

Question 14

A cell with a volume of $$1,000\ \mu	ext{m}^3 is $$most likely which of the following cell types?

Accepted Answer

Beta cell

Question 15

Which of the following is the correct form of Hooke's Law for the force exerted by a spring?

Accepted Answer

$$F = -kx$$

Question 16

If the cross-sectional area $$A in $$Fick's Law is doubled while all other variables remain constant, what happens to the rate of diffusion $$\frac{N}{\Delta t}$$?

Accepted Answer

It is doubled

Cell Size, Diffusion, and Simple Harmonic Motion: Physics with Calculus Study Notes

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