Q: A 70-kg person jumps from a height of $56$ cm. Using $g = 9.8\ \mathrm{m/s^2}$, what is the velocity on impact with the ground?

$v = \sqrt{2 \times 9.8 \times 0.56} \approx 3.32\ \mathrm{m/s}$

Q: A 70-kg person in a car crash is stopped by an airbag over a distance of $30$ cm from an initial velocity of $20$ m/s. What is the average deceleration?

$a = \dfrac{v^2}{2s} = \dfrac{(20)^2}{2 \times 0.3} = 666.7\ \mathrm{m/s^2}$

Q: A spring is stretched by $0.05$ m and has a spring constant $K = 200$ N/m. What is the potential energy stored in the spring?

$E = \dfrac{1}{2} \times 200 \times (0.05)^2 = 0.25\ \mathrm{J}$

Question 1

Which of the following best defines Young's modulus $Y$ for a material?

Accepted Answer

The ratio of stress to strain within the elastic limit of the material.

Question 2

A steel rod of length $l$ and cross-sectional area $A$ is subjected to a force $F$ causing an elongation $\Delta l$. Which equation correctly expresses the longitudinal strain $S_l$?

Accepted Answer

$S_l = \dfrac{\Delta l}{l}$

Question 3

A spring with spring constant $K$ is stretched by $\Delta l$. What is the potential energy stored in the spring?

Accepted Answer

$E = \dfrac{1}{2} K \Delta l^2$

Question 4

If a bone with area $A$ and length $l$ has a breaking stress $S_B$ and Young's modulus $Y$, what is the force $F_B$ required to fracture the bone?

Accepted Answer

$F_B = S_B A$

Question 5

A person of mass $m$ falls from a height $h$. What is their velocity $v$ just before impact with the ground?

Accepted Answer

$v = \sqrt{2gh}$

Question 6

The energy stored in a compressed bone at the point of fracture is given by $E = \dfrac{1}{2} \dfrac{A l S_B^2}{Y}$. Which variable, if doubled, would result in the greatest increase in $E$?

Accepted Answer

Doubling $S_B$ (breaking stress)

Question 7

In a car crash, an airbag increases the stopping distance for a passenger from $2$ cm to $30$ cm. How does this affect the average stopping force, assuming the initial velocity is unchanged?

Accepted Answer

The average stopping force decreases.

Question 8

A 70-kg person jumps from a height of $56$ cm. Using $g = 9.8\ \mathrm{m/s^2}$, what is the velocity on impact with the ground?

Accepted Answer

$v = \sqrt{2 	imes 9.8 	imes 0.56} \approx 3.32\ \mathrm{m/s}$

Question 9

Which of the following best describes the relationship between stress $S$ and strain $S_l$ in the elastic region of a material?

Accepted Answer

$S$ is proportional to $S_l$

Question 10

A bone with area $A = 6\ \mathrm{cm^2}$, length $l = 90\ \mathrm{cm}$, breaking stress $S_B = 10^6\ \mathrm{dyn/cm^2}$, and Young's modulus $Y = 14 	imes 10^{10}\ \mathrm{dyn/cm^2}$ absorbs how much energy at the point of compressive fracture?

Accepted Answer

$E = 192.5\ \mathrm{J}$

Question 11

Which equation correctly gives the average impulsive force $F_{av}$ exerted during a collision, given the change in momentum and the time interval $\Delta t$?

Accepted Answer

$F_{av} = \dfrac{mv_f - mv_i}{\Delta t}$

Question 12

A stretched elastic body is analogous to a spring with spring constant $K$. Which formula relates $K$ to Young's modulus $Y$, area $A$, and length $l$?

Accepted Answer

$K = Y \dfrac{A}{l}$

Question 13

If the stopping distance in a car crash is doubled, what happens to the average force experienced by the passenger, assuming the initial velocity is unchanged?

Accepted Answer

It is halved.

Question 14

Which of the following is a correct expression for the compression $\Delta l$ at the breaking point of a bone?

Accepted Answer

$\Delta l = \dfrac{S_B l}{Y}$

Question 15

A 70-kg person in a car crash is stopped by an airbag over a distance of $30$ cm from an initial velocity of $20$ m/s. What is the average deceleration?

Accepted Answer

$a = \dfrac{v^2}{2s} = \dfrac{(20)^2}{2 	imes 0.3} = 666.7\ \mathrm{m/s^2}$

Question 16

Which of the following statements about impulsive force is correct?

Accepted Answer

The average value of the impulsive force can be calculated using the change in momentum over the time interval.

Question 17

A spring is stretched by $0.05$ m and has a spring constant $K = 200$ N/m. What is the potential energy stored in the spring?

Accepted Answer

$E = \dfrac{1}{2} 	imes 200 	imes (0.05)^2 = 0.25\ \mathrm{J}$

Question 18

Which of the following best explains why airbags reduce injuries in car accidents?

Accepted Answer

They increase the stopping time, thereby reducing the average force.

Question 19

If the Young's modulus $Y$ of a material increases, what happens to the elongation $\Delta l$ produced by a given force $F$?

Accepted Answer

Elongation decreases.

Elasticity and Strength of Materials: Biophysics Applications

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