Question 1

Which of the following best describes the role of models in physics, especially when applied to biological systems?

Accepted Answer

A model is a simplified picture of reality that still captures the essence of what you want to study.

Question 2

A large number of molecules start at the origin and undergo a random walk along the x-axis, each step being a distance $$d in a $$random direction. After 100 steps, what is the most likely final position of a molecule?

Accepted Answer

$$x = 0$$

Question 3

After 100 steps of a random walk, each of length $$d$$, what is the diffusion distance from the origin?

Accepted Answer

$$60d$$

Question 4

The root mean square (rms) distance for a random walk is used to measure the spread of molecules. Which formula correctly expresses the rms distance after $$n$$ steps of length $$d$$?

Accepted Answer

$$x_{rms} = d\sqrt{n}$$

Question 5

If the force between two ions is $$1.00 nN $$and the distance between them doubles, what is the new force, given that electric force scales inversely as the square of the distance?

Accepted Answer

$$0.25 nN$$

Question 6

The diffusion coefficient $$D$$ for small molecules in water is estimated using $$D = \frac{1}{2}vd$$, where $$v is $$molecular speed and $$d is $$step size. If the same type of reasoning is applied to diffusion through air, how does $$D$$ compare to that in water?

Accepted Answer

Larger than in water

Question 7

An animal's mass $$m is $$proportional to the cube of some linear dimension $$l. If $$the strength of its bones is proportional to the square of $$l$$, how must bone diameter scale with animal size to support increased mass?

Accepted Answer

Bone diameter must scale faster than $$l$$, specifically as $$l^{3/2}$$

Question 8

Basal metabolic rate (BMR) for mammals scales with mass $$m as$$ $$BMR \propto m^r. If a log-log $$graph of BMR vs. mass has a slope of $$0.75$$, what is the scaling law?

Accepted Answer

$$BMR \propto m$$^{0.75}$$

Question 9

If a 500-kg horse has a resting heart rate of 38 beats/min, and heart rate $$R$$ scales with mass $$m as$$ $$R \propto m$$^{-0.25}$$, what is the expected heart rate of an 80-g hamster?

Accepted Answer

About 1150 beats/min

Question 10

Which of the following is NOT a major goal for students in a physics for life sciences course?

Accepted Answer

Memorize all equations without understanding their application

Question 11

Which property of logarithms allows you to convert a power law $$Y = CX^r$$ into a linear relationship on a log-log graph?

Accepted Answer

$$\log(a^n) = n\log(a)$$

Question 12

In the context of diffusion, why does the diffusion distance increase much more slowly than the maximum possible travel distance as the number of steps increases?

Accepted Answer

Because the diffusion distance increases with the square root of the number of steps

Question 13

Which of the following best describes the difference between descriptive and explanatory models in physics?

Accepted Answer

Descriptive models examine essential characteristics and properties, while explanatory models examine causes.

Question 14

Suppose the average position of molecules after a random walk is $$x = 0. $$Why is the rms (root mean square) distance a better measure of their spread?

Accepted Answer

Because the rms distance measures the average squared position, reflecting the spread

Question 15

Which of the following is an example of ratio reasoning in physics?

Accepted Answer

Comparing ratios to draw conclusions without knowing the proportionality constant

Question 16

If the step size $$d$$ for a molecule in air is much larger than in water, but the molecular speed $$v is $$about the same, what happens to the diffusion coefficient $$D in $$air compared to water?

Accepted Answer

It increases

Question 17

Which of the following statements about scaling laws in biology is correct?

Accepted Answer

Scaling laws are often expressed as power laws and visualized using log-log graphs

Question 18

A scientist wants to model the diffusion of a drug molecule in the bloodstream. Which type of model would best help her understand the underlying causes of the molecule's movement?

Accepted Answer

An explanatory model

Question 19

Which of the following is a real-world example of applying physics principles to biological systems?

Accepted Answer

Calculating the force required for a cheetah to accelerate during a chase

Physics for the Life Sciences: Foundations and Quantitative Reasoning

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