Question 1

A spherical cell of type A has a surface area of $$2\ \mu m^2$. If a type B cell has a diameter three times that of type A, what is the surface area of type B?

Accepted Answer

$$18\ \mu m^2$

Question 2

If Angela walks to work in $$15$$ minutes at a steady speed, how long will it take her to cycle the same distance if she cycles three times as fast as she walks?

Accepted Answer

$$5$$ minutes

Question 3

The basal metabolic rate (BMR) of mammals scales with mass $$m as$$ $$BMR = C m$$^{3/4}$$. If a mouse has a mass of 0.02$$\ kg$$ and a BMR of 0.1$$\ W$$, what is the expected BMR of a mammal with mass 2$$\ kg$$?

Accepted Answer

$$0.56\ W$$

Question 4

Which of the following best describes the difference between a descriptive and an explanatory model in physics?

Accepted Answer

Descriptive models simplify and characterize phenomena; explanatory models provide causal mechanisms and predictive power.

Question 5

If the force between two ions is $$3.00\ N at a $$distance $$r$$, what will the force be if the distance doubles, given that force scales inversely with the square of the distance?

Accepted Answer

$$0.75\ N$$

Question 6

On a log-log graph, the relationship $$Y = C X^n$$ appears as:

Accepted Answer

A straight line with slope $$n$$

Question 7

If the heart rate $$R of $$mammals scales as $$R = C m$$^{-1/4}$$, and a horse (1200$$\ kg$$) has a heart rate of 38$ beats/min, what is the expected heart rate of an 80$$\ g$$ hamster?

Accepted Answer

$$420$$ beats/min

Question 8

Which of the following is a correct statement about the scaling of bone strength and animal mass?

Accepted Answer

Bone strength scales with the square of the animal's linear dimension, while mass scales with the cube.

Question 9

If the average lifetime $$T of a $$mammal scales as $$T \propto m$$^{1/4}$$ and heart rate R$$ \propto $$m^{-1/4}$$, how does the total number of heartbeats in a lifetime $$N$$ scale with mass $$m$$?

Accepted Answer

$$N \propto m$$^{0}$$

Question 10

Which of the following is NOT a fundamental physical quantity?

Accepted Answer

Force

Question 11

A model in physics is best described as:

Accepted Answer

A simplified description that captures the essence of a system for analysis.

Question 12

If the surface area $$A of a $$sphere is proportional to the square of its radius $$r$$, what happens to the surface area if the radius is doubled?

Accepted Answer

It increases by a factor of $$4$$

Question 13

Which of the following best explains why large animals like elephants have much thicker legs relative to their body size than small animals like shrews?

Accepted Answer

Because bone strength scales with area ($$l^2) $$while mass scales with volume ($$l^3$$), so larger animals need disproportionately thicker bones.

Question 14

Which of the following is a correct use of ratio reasoning in proportional relationships?

Accepted Answer

If $$y = Cx^n$$, then $$\frac{y_2$}{y_1$} = \left(\frac{x_2$}{x_1$}\right)^n$$

Question 15

Which of Newton's Laws explains why a sprinter accelerates forward when pushing off the starting blocks?

Accepted Answer

Third Law (Action-Reaction)

Question 16

Which of the following is true about the use of log-log graphs in biology?

Accepted Answer

They are used to linearize power-law relationships for easier analysis.

Scaling Laws, Models, and Quantitative Reasoning in Physics for the Life Sciences

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