Q: A 2-meter-long steel rod with a cross-sectional area of $$1.0 \ \mathrm{cm}^2 is $$stretched by a force of $$10,000 \ \mathrm{N}. If $$the Young's modulus for steel is $$2.0 \times 10$$^{11}$$ \ \mathrm{N/m}^2$$, what is the elongation $$\Delta l of $$the rod?

$$\Delta l = 1.0 \times 10$$^{-3}$$ \ \mathrm{m}$$

Question 1

A uniform horizontal beam is supported at its ends and sags under its own weight. Which of the following best describes the stresses experienced by the beam?

Accepted Answer

The top of the beam is under compression, and the bottom is under tension.

Question 2

Which of the following is a necessary condition for an object to be in static equilibrium?

Accepted Answer

The sum of all external torques about any point must be zero.

Question 3

A 2-meter-long steel rod with a cross-sectional area of $$1.0 \ \mathrm{cm}^2 is $$stretched by a force of $$10,000 \ \mathrm{N}. If $$the Young's modulus for steel is $$2.0 	imes 10$$^{11}$$ \ \mathrm{N/m}^2$$, what is the elongation $$\Delta l of $$the rod?

Accepted Answer

$$\Delta l = 1.0 	imes 10$$^{-3}$$ \ \mathrm{m}$$

Question 4

Which of the following statements about the center of gravity is correct?

Accepted Answer

The center of gravity is the point where the entire weight of the object can be considered to act.

Question 5

A car is parked on a hill. Under what condition will the car tip over rather than slide down the hill?

Accepted Answer

When the center of gravity is outside the area of support.

Question 6

Which equation correctly expresses the first condition for equilibrium?

Accepted Answer

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

Question 7

A diver experiences a pressure increase as they descend underwater. This is an example of which type of stress?

Accepted Answer

Bulk stress

Question 8

A wire is stretched by a force $$F$$ and its length increases by $$\Delta l. If $$the original length is $$l_0$$ and the cross-sectional area is $$A$$, what is the expression for Young's modulus $$Y$$?

Accepted Answer

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

Question 9

Which of the following best describes the difference between elastic and plastic deformation?

Accepted Answer

Elastic deformation is reversible, while plastic deformation is permanent.

Question 10

A cube of material is subjected to a shear force $$F$$ parallel to its top surface, causing a displacement $$x. If $$the height of the cube is $$h$$ and the area of the top surface is $$A$$, what is the shear modulus $$S$$?

Accepted Answer

$$S = \frac{F/A}{x/h}$$

Question 11

A submarine descends to a depth where the pressure increases by $$2.0 	imes 10^7$ \ \mathrm{Pa}. If $$the bulk modulus of the hull material is $$1.0 	imes 10$$^{11}$$ \ \mathrm{N/m}^2$$, what is the fractional decrease in volume $$\frac{\Delta V}{V_0$}$$?

Accepted Answer

$$2.0 	imes 10$$^{-4}$$

Question 12

Which of the following is true about the breaking stress of a material?

Accepted Answer

It is the stress required to cause actual fracture of a material.

Question 13

A mug is suspended from two different points and vertical lines are drawn from each suspension point. Where do these lines intersect?

Accepted Answer

At the center of gravity of the mug

Question 14

Which of the following best describes the proportional limit on a stress-strain curve?

Accepted Answer

The point up to which stress and strain are proportional

Question 15

If the compressibility $$k of a $$material is the reciprocal of its bulk modulus $$B$$, which equation is correct?

Accepted Answer

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

Question 16

A guitar string is stretched by a force $$F$$ and has a cross-sectional area $$A. $$What is the tensile stress in the string?

Accepted Answer

$$\frac{F}{A}$$

Question 17

Which of the following is NOT a correct step in solving a static equilibrium problem?

Accepted Answer

Ignore the direction of forces when calculating torques.

Question 18

A ribbon is cut by scissors, which applies a force parallel to the surface of the ribbon. What type of stress is primarily responsible for the deformation?

Accepted Answer

Shear stress

Question 19

Which of the following is true about the center of gravity and stability of an object?

Accepted Answer

An object is not in equilibrium if its center of gravity lies outside the area of support.

Equilibrium and Elasticity: Structured Study Notes

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