Q: Which formula defines tensile stress in a stretched rod?

$$\text{Tensile stress} = \frac{F}{A}$$

Question 1

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

Accepted Answer

Both the net force and the net torque on the object must be zero.

Question 2

A painter stands on a ladder and leans out to the side. According to the principles of stability, what will happen if his center of gravity moves outside the ladder's base of support?

Accepted Answer

The ladder will tip over.

Question 3

Which equation correctly expresses Hooke's Law for a spring?

Accepted Answer

$$F = -k \Delta x$$

Question 4

A 10.2 kg block is suspended from a spring with a spring constant $$k = 5000\ \mathrm{N/m}. $$What is the extension $$\Delta y of $$the spring due to the block's weight? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta y = 0.02\ \mathrm{m}$$

Question 5

Which material listed below has the highest Young's modulus, indicating the greatest stiffness?

Accepted Answer

Steel

Question 6

A steel rod of length $$L$$ and cross-sectional area $$A is $$stretched by a force $$F. $$Which equation gives the change in length $$\Delta L$$ using Young's modulus $$Y$$?

Accepted Answer

$$\Delta L = \frac{F L}{A Y}$$

Question 7

If a material is stretched beyond its elastic limit, what happens to its deformation?

Accepted Answer

It becomes permanently deformed.

Question 8

Which of the following best describes the difference between 'rigid' and 'pliant' materials?

Accepted Answer

Rigid materials show small deformations under normal forces; pliant materials show large deformations with small forces.

Question 9

A spring is stretched by $$\Delta x = 0.05\ \mathrm{m}$$ and exerts a restoring force of $$F = -250\ \mathrm{N}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = 5,000\ \mathrm{N/m}$$

Question 10

Which of the following statements about static equilibrium is correct?

Accepted Answer

An object in static equilibrium must have both net force and net torque equal to zero.

Question 11

A gymnast balances on one hand. For maximum stability, where should her center of gravity be located?

Accepted Answer

Directly above her hand (base of support)

Question 12

Which formula defines tensile stress in a stretched rod?

Accepted Answer

$$	ext{Tensile stress} = \frac{F}{A}$$

Question 13

A rubber band is stretched with a small force and shows a large deformation. What property does this illustrate?

Accepted Answer

High pliancy

Question 14

A 61 kg woman stands on tiptoe, with her foot making a $$25^\circ$$ angle with the floor. If the tension in her Achilles tendon is $$1800\ \mathrm{N}$$, what fraction does this force exceed her weight?

Accepted Answer

$$\frac{1800}{600} = 3$$ times her weight

Question 15

Which of the following is true about the elastic region of a material's stress-strain curve?

Accepted Answer

The material returns to its original length when the force is removed.

Question 16

A steel rod with $$Y = 20\ \mathrm{GPa} is $$stretched by a force $$F. If $$the cross-sectional area is doubled, what happens to the change in length $$\Delta L$$ for the same force?

Accepted Answer

$$\Delta L$$ halves

Question 17

Which of the following is a real-world example of torque in the human body?

Accepted Answer

The force exerted by the Achilles tendon when standing on tiptoe

Question 18

If a spring obeys Hooke's Law, what is the relationship between the restoring force and the displacement?

Accepted Answer

The restoring force is proportional to the displacement and acts in the opposite direction.

Question 19

Which of the following would increase the stability of an object?

Accepted Answer

Lowering its center of gravity and broadening its base of support

Chapter 8: Equilibrium and Elasticity – Study Notes

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