Q: A tendon has a Young’s modulus of $$1.2 \times 10^9$ Pa. If a force of 1200$ N is applied to a tendon with cross-sectional area 1$$ \times $$10^{-4} m$^2$$ and original length $$0.1 m$$, what is the elongation $$\Delta l$$?

$$\Delta l = \frac{F l_0$}{Y A} = \frac{1200 \times 0.1}{1.2 \times 10^9$ \times 1 \times 10$$^{-4}$$} = 0.001 m$$

Question 1

A Roman aqueduct uses arches to sustain the weight of the structure and the water it carries. Which principle of physics is primarily responsible for the stability of the arch?

Accepted Answer

The arch distributes compressive forces, allowing the structure to remain in equilibrium.

Question 2

Which equation represents the first condition for equilibrium for a rigid body?

Accepted Answer

$$\sum \vec{F} = 0$$

Question 3

A body is acted upon by three forces: two upward forces of $$F$$ each and one downward force of $$2F. $$What can be said about the equilibrium of the body?

Accepted Answer

Both the net force and net torque are zero; the body is in static equilibrium.

Question 4

Which equation represents the second condition for equilibrium for a rigid body?

Accepted Answer

$$\sum \vec{	au} = 0$$

Question 5

A car is parked on an incline. Under what condition will the car remain in equilibrium?

Accepted Answer

The center of gravity must be over the area of support.

Question 6

If the center of gravity of a body lies outside the area bounded by its supports, what will happen?

Accepted Answer

The body will tip over and not be in equilibrium.

Question 7

Which of the following best describes Young’s modulus?

Accepted Answer

Young’s modulus is the ratio of tensile stress to tensile strain.

Question 8

A steel rod with original length $$l_0$$ and cross-sectional area $$A is $$stretched by a force $$F. If $$the elongation is $$\Delta l$$, what is the formula for Young’s modulus $$Y$$?

Accepted Answer

$$Y = \frac{F l_0$}{A \Delta l}$$

Question 9

A diver experiences bulk stress due to water pressure. Which modulus is used to describe the material’s response to this type of stress?

Accepted Answer

Bulk modulus

Question 10

Which equation defines compressibility $$k in $$terms of bulk modulus $$B$$?

Accepted Answer

$$k = \frac{1}{B}$$

Question 11

A ribbon is cut by scissors, experiencing deformation. What type of stress is primarily involved?

Accepted Answer

Shear stress

Question 12

A beam supported at both ends sags under its own weight. Which part of the beam is under tension?

Accepted Answer

The bottom of the beam

Question 13

Which formula represents shear modulus $$S$$ for a material?

Accepted Answer

$$S = \frac{F_{\parallel}/A}{x/h}$$

Question 14

Which material has the highest Young’s modulus according to the provided table?

Accepted Answer

Steel

Question 15

A stress-strain diagram for vulcanized rubber shows elastic hysteresis. What does this mean?

Accepted Answer

The stress-strain curve for increasing stress differs from that for decreasing stress.

Question 16

A ductile metal is stretched beyond its elastic limit. What type of deformation occurs?

Accepted Answer

Plastic deformation

Question 17

Which of the following best describes the breaking stress of a material?

Accepted Answer

The stress required to cause actual fracture of the material.

Question 18

An anglerfish survives at depths where the pressure is about 100 atmospheres. What property allows it to withstand such bulk stress?

Accepted Answer

It has no internal air spaces.

Question 19

A tendon has a Young’s modulus of $$1.2 	imes 10^9$ Pa. If a force of 1200$ N is applied to a tendon with cross-sectional area 1$$ 	imes $$10^{-4} m$^2$$ and original length $$0.1 m$$, what is the elongation $$\Delta l$$?

Accepted Answer

$$\Delta l = \frac{F l_0$}{Y A} = \frac{1200 	imes 0.1}{1.2 	imes 10^9$ 	imes 1 	imes 10$$^{-4}$$} = 0.001 m$$

Equilibrium and Elasticity: Structured Study Notes

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