Q: A water tank is 10 m above a faucet in a house. What is the difference in water pressure between the faucet and the surface of the water in the tank? (Assume $$\rho_{water} = 1000 \ \mathrm{kg/m^3$}$$, $$g = 9.8 \ \mathrm{m/s^2$})$$

$$\Delta P = \rho g h = 1000 \times 9.8 \times 10 = 98,000 \ \mathrm{Pa}$$

Question 1

A diver is swimming at a depth $$h$$ below the surface of the ocean. If the density of seawater is $$\rho$$ and atmospheric pressure is $$P_0$$, what is the total pressure experienced by the diver at that depth?

Accepted Answer

$$P = P_0$ + \rho g h$$

Question 2

Which of the following best describes the condition for equilibrium in a static structure?

Accepted Answer

Net force and net torque on the structure are zero

Question 3

A steel wire of length $$L$$ and cross-sectional area $$A is $$stretched by a force $$F$$, causing an elongation $$\Delta l. $$Which equation relates these quantities using Young's modulus $$E$$?

Accepted Answer

$$\Delta l = \frac{F L}{A E}$$

Question 4

Which statement correctly describes the difference between the proportional limit and the elastic limit in a stress-strain curve?

Accepted Answer

Beyond the proportional limit, the material is still elastic but not linear; beyond the elastic limit, permanent deformation occurs.

Question 5

A small air bubble rises from the bottom of a lake to the surface. What happens to its diameter as it ascends, and why?

Accepted Answer

The diameter increases because the pressure decreases as the bubble rises.

Question 6

A 1.60-m-long steel piano wire with a diameter of 0.20 cm stretches by 0.25 cm when tightened. If the Young's modulus for steel is $$2.0 	imes 10$$^{11}$$ \ \mathrm{N/m^2$}$$, what is the tension in the wire?

Accepted Answer

$$F = \frac{A E \Delta l}{L}$$

Question 7

Which type of stress is responsible for stretching an object, and how is it defined?

Accepted Answer

Tensile stress, defined as force per unit area acting to stretch the object

Question 8

A column in a building is subjected to inward forces on its ends, causing a change in volume. Which modulus describes this behavior?

Accepted Answer

Bulk modulus

Question 9

A truss bridge is designed so that each member is under either tension or compression. Why is it important to keep the anticipated stress below 1/3 to 1/4 of the ultimate strength?

Accepted Answer

To ensure safety and prevent structural failure due to unexpected loads or material flaws

Question 10

Three containers are filled with water to the same height and have the same surface area at the base, but different shapes and total water weights. Which container has the greatest total force acting on its base?

Accepted Answer

All three are equal, because force depends only on height and area, not shape or total weight

Question 11

A person falls through thin ice on a frozen lake. Which strategy minimizes the pressure exerted on the ice and increases the chance of escape?

Accepted Answer

Lie down flat and crawl toward shore

Question 12

The pressure at a depth $$h in a $$fluid of density $$\rho is $$given by $$P = P_0$ + \rho g h. If $$the density of the fluid increases, what happens to the pressure at a given depth?

Accepted Answer

Pressure increases

Question 13

Which of the following is the correct definition of stress in the context of elasticity?

Accepted Answer

Stress is the force per unit area applied to an object

Question 14

A suspension bridge uses cables to support the roadway. If the weight of the roadway is uniformly distributed, what is the shape of the cable between the towers?

Accepted Answer

A parabola

Question 15

Which equation defines the density $$\rho of a $$substance?

Accepted Answer

$$\rho = \frac{m}{V}$$

Question 16

A steel wire fractures when the applied tensile stress exceeds its ultimate tensile strength. If the cross-sectional area of the wire is $$A$$ and the ultimate tensile strength is $$\sigma_{ult}$$, what is the maximum force $$F_{max}$$ the wire can withstand before breaking?

Accepted Answer

$$F_{max} = A \sigma_{ult}$$

Question 17

Which modulus describes the resistance of a material to shape changes under shear stress?

Accepted Answer

Shear modulus

Question 18

A water tank is 10 m above a faucet in a house. What is the difference in water pressure between the faucet and the surface of the water in the tank? (Assume $$\rho_{water} = 1000 \ \mathrm{kg/m^3$}$$, $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta P = ho g h = 1000 	imes 9.8 	imes 10 = 98,000 \ \mathrm{Pa}$$

Question 19

Which of the following statements about pressure in a static fluid is correct?

Accepted Answer

Pressure is the same in every direction at a given depth

Elasticity, Stress, Strain, and Fluid Pressure: Study Notes

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