Q: A block of wood with mass $$m = 0.5\ \mathrm{kg}$$ and volume $$V = 0.001\ \mathrm{m}^3$$ floats in water. What is the fraction of the block's volume that is submerged?

$$\dfrac{m}{\rho_{\mathrm{water}} V} = \dfrac{0.5}{1000 \times 0.001} = 0.5$$

Q: A diver is 20 meters below the surface of the ocean. If the density of seawater is $$\rho = 1025\ \mathrm{kg/m}^3$$ and $$g = 9.8\ \mathrm{m/s}^2$$, what is the gauge pressure at this depth?

$$P = 1025 \times 9.8 \times 20 = 200,900\ \mathrm{Pa}$$

Question 1

Which of the following statements correctly describes the difference between a liquid and a gas?

Accepted Answer

A liquid has a fixed volume but can take any shape, while a gas can be easily compressed and take any shape.

Question 2

A block of wood with mass $$m = 0.5\ \mathrm{kg}$$ and volume $$V = 0.001\ \mathrm{m}^3$$ floats in water. What is the fraction of the block's volume that is submerged?

Accepted Answer

$$\dfrac{m}{ho_{\mathrm{water}} V} = \dfrac{0.5}{1000 	imes 0.001} = 0.5$$

Question 3

Which device is used to measure atmospheric pressure and is based on the height of a column of mercury?

Accepted Answer

Mercury barometer

Question 4

A hydraulic lift uses a small piston of area $$A_1$$ and a large piston of area $$A_2. If a $$force $$F_1 is $$applied to the small piston, what is the force $$F_2$$ exerted by the large piston, assuming the fluid is incompressible and at equilibrium?

Accepted Answer

$$F_2$$ = \dfrac{$$A_2$$}{$$A_1$$} $$F_1$$

Question 5

A diver is 20 meters below the surface of the ocean. If the density of seawater is $$\rho = 1025\ \mathrm{kg/m}^3$$ and $$g = 9.8\ \mathrm{m/s}^2$$, what is the gauge pressure at this depth?

Accepted Answer

$$P = 1025 	imes 9.8 	imes 20 = 200,900\ \mathrm{Pa}$$

Question 6

A U-tube contains water in one arm and oil in the other. The oil column is higher than the water column. What can you conclude about the density of the oil compared to water?

Accepted Answer

The oil is less dense than water.

Question 7

A tire pressure gauge reads 250 kPa. If atmospheric pressure is 101 kPa, what is the absolute pressure inside the tire?

Accepted Answer

$$P = 250\ \mathrm{kPa} + 101\ \mathrm{kPa} = 351\ \mathrm{kPa}$$

Question 8

A block of steel and a block of aluminum, both with the same volume, are fully submerged in water. Which experiences the greater buoyant force?

Accepted Answer

Both experience the same buoyant force

Question 9

A wooden ball floats in water so that half of its volume is submerged. What is the magnitude of the buoyant force acting on the ball?

Accepted Answer

Exactly the ball's weight

Question 10

A helium balloon of radius $$R is $$anchored to the ground with a rope. The mass of the balloon and basket is $$m$$, and the cargo has mass $$M. $$The density of air is $$\rho_{\mathrm{air}}$$, and the density of helium is $$\rho_{\mathrm{He}}. $$What is the tension $$T in $$the rope anchoring the balloon?

Accepted Answer

$$T = (m + M)g + \rho_{\mathrm{He}} V g - \rho_{\mathrm{air}} V g$$

Question 11

Which of the following best explains why hot-air balloons rise?

Accepted Answer

The density of the hot air inside the balloon is less than the density of the surrounding air, resulting in a net upward buoyant force.

Question 12

Water flows through a horizontal pipe that narrows from area $$A_1 to$$ $$A_2. If $$the velocity in the wide section is $$v_1$$, what is the velocity $$v_2 in $$the narrow section?

Accepted Answer

$$v_2$$ = \dfrac{$$A_1$$}{$$A_2$$} $$v_1$$

Question 13

According to Bernoulli's equation, what happens to the pressure in a fluid as its speed increases?

Accepted Answer

Pressure decreases

Question 14

A water tank is open to the atmosphere at the top. Water flows out of a hole at the bottom. If the height difference between the water surface and the hole is $$h$$, what is the speed $$v of $$the water exiting the hole according to Torricelli’s theorem?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 15

A patient’s blood pressure is measured using a manometer. If the column of mercury rises to 120 mm, what is the pressure in pascals? (Density of mercury $$= 13,600\ \mathrm{kg/m}^3$$, $$g = 9.8\ \mathrm{m/s}^2)$$

Accepted Answer

$$P = 0.12 	imes 13,600 	imes 9.8 = 16,012\ \mathrm{Pa}$$

Question 16

Which of the following is true about pressure in a fluid at rest?

Accepted Answer

Pressure is the same in every direction at a given depth.

Question 17

A baseball is thrown with a spin, causing the air to move faster over one side of the ball than the other. According to Bernoulli’s principle, what effect does this have?

Accepted Answer

The pressure is lower on the side where the air moves faster, causing the ball to curve.

Question 18

A hospital uses a hydraulic lift to raise a patient. If the input piston has an area of $$0.01\ \mathrm{m}^2$$ and the output piston has an area of $$0.5\ \mathrm{m}^2$$, what force must be applied to the input piston to lift a $$500\ \mathrm{N}$$ patient?

Accepted Answer

$$F = \dfrac{0.01}{0.5} 	imes 500 = 10\ \mathrm{N}$$

Chapter 10: Fluids – Physics Study Notes

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