Question 1

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

Accepted Answer

The vector sum of all external forces acting on the arch must be zero: $$\sum \vec{F} = 0$$

Question 2

A body is in static equilibrium if which two conditions are satisfied?

Accepted Answer

The vector sum of all external forces is zero and the sum of all external torques is zero: $$\sum \vec{F} = 0$$ and $$\sum 	au = 0$$

Question 3

A car parked on a slope is in equilibrium as long as its center of gravity is:

Accepted Answer

Over the area of support provided by the wheels.

Question 4

A mug is suspended from two different points. The vertical lines from each suspension point intersect at a single location inside the mug. What does this intersection represent?

Accepted Answer

The center of gravity of the mug.

Question 5

A beam supported at both ends sags under its own weight. Which type of stress is experienced at the top and bottom of the beam?

Accepted Answer

The top is under compressive stress, and the bottom is under tensile stress.

Question 6

A diver experiences bulk stress due to water pressure. Which modulus describes the diver's resistance to compression?

Accepted Answer

Bulk modulus $$B$$

Question 7

A guitar string is stretched by forces acting at its ends. What type of stress and strain does it experience?

Accepted Answer

Tensile stress and tensile strain

Question 8

A human anterior tibial tendon has a Young’s modulus of $$1.2 	imes 10^9$ Pa. If a force of 120$ N is applied to a tendon with cross-sectional area 1$$ 	ext{ cm}^2$$ and original length 10$ cm, what is the elongation $$\Delta l$$? (Use Y$$ = \frac{F $$l_0$$}{A \Delta l}$$)

Accepted Answer

$$\Delta l = 0.01 cm$$

Question 9

Which equation correctly defines compressibility $$k in $$terms of bulk modulus $$B$$ and volume change?

Accepted Answer

$$k = \frac{1}{B} = -\frac{\Delta V / V_0$}{\Delta p}$$

Question 10

A ribbon is cut by scissors, experiencing shear stress. Which formula gives the shear modulus $$S$$?

Accepted Answer

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

Question 11

Which material listed below has the highest Young’s modulus, indicating the greatest resistance to deformation under tension?

Accepted Answer

Steel

Question 12

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 13

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

Accepted Answer

Plastic deformation

Question 14

If a material is subjected to a stress greater than its breaking stress, what happens?

Accepted Answer

The material fractures.

Question 15

An anglerfish survives at ocean 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 16

A car tips over when its center of gravity is outside the area of support. What effect does raising the center of gravity have?

Accepted Answer

It decreases the incline needed to tip the vehicle.

Question 17

A block is subjected to a force perpendicular to its cross-sectional area, causing it to elongate. Which formula gives the tensile strain?

Accepted Answer

$$	ext{Tensile strain} = \frac{\Delta l}{l_0$}$$

Question 18

Which of the following is NOT a condition for static equilibrium?

Accepted Answer

The sum of internal forces must be zero.

Question 19

A liquid with a high compressibility $$k$$ will:

Accepted Answer

Change its volume significantly under pressure.

Equilibrium and Elasticity: Structured Study Notes

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