Q: A sealed balloon contains 2.0 moles of helium gas at a temperature of $$300\ \mathrm{K}$$ and occupies a volume of $$24.6\ \mathrm{L}. $$Using the ideal gas law $$PV = nRT$$, what is the pressure inside the balloon? (Use $$R = 0.0821\ \mathrm{L\ atm\ $$mol^{-1}$$\ K$$^{-1}$$})$$

$$P = \dfrac{nRT}{V} = \dfrac{2.0 \times 0.0821 \times 300}{24.6} = 1.999\ \mathrm{atm}$$

Q: A polar bear weighing $$500\ \mathrm{kg}$$ stands on a sheet of ice that is $$0.5\ \mathrm{m}$$ thick. If the density of ice is $$900\ \mathrm{kg/m^3$}$$, what is the minimum area of ice needed to support the bear without sinking? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$A = \dfrac{mg}{\rho_{ice} \cdot g \cdot d} = \dfrac{500}{900 \times 0.5} = 1.11\ \mathrm{m^2$}$$

Q: A water tower is open to the atmosphere at the top and connected to a pipe at the bottom. If the height difference between the water surface and the pipe outlet is $$15\ \mathrm{m}$$, what is the pressure difference between the top and the bottom of the tower? (Density of water $$= 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

$$\Delta P = \rho g h = 1000 \times 9.8 \times 15 = 147,000\ \mathrm{Pa}$$

Question 1

A block of wood with a density less than water is placed in a tank of water. Which of the following statements best describes the buoyant force acting on the block?

Accepted Answer

The buoyant force equals the weight of the water displaced by the block.

Question 2

A sealed balloon contains 2.0 moles of helium gas at a temperature of $$300\ \mathrm{K}$$ and occupies a volume of $$24.6\ \mathrm{L}. $$Using the ideal gas law $$PV = nRT$$, what is the pressure inside the balloon? (Use $$R = 0.0821\ \mathrm{L\ atm\ $$mol^{-1}$$\ K$$^{-1}$$})$$

Accepted Answer

$$P = \dfrac{nRT}{V} = \dfrac{2.0 	imes 0.0821 	imes 300}{24.6} = 1.999\ \mathrm{atm}$$

Question 3

According to Pascal's Principle, if a force is applied to a confined fluid, how is the pressure transmitted?

Accepted Answer

The pressure is transmitted equally in all directions throughout the fluid.

Question 4

A $$50\ \mathrm{g}$$ ice cube at $$0^\circ\mathrm{C} is $$placed in $$200\ \mathrm{g} of $$water at $$20^\circ\mathrm{C}. $$How much ice will melt before thermal equilibrium is reached? (Latent heat of fusion for ice $$L_f = 334\ \mathrm{J/g}$$, specific heat of water $$c = 4.18\ \mathrm{J/g\ ^\circ C})$$

Accepted Answer

All $$50\ \mathrm{g} of $$ice will melt.

Question 5

A $$100\ \mathrm{g}$$ mug of coffee at $$90^\circ\mathrm{C} is $$left in a $$20^\circ\mathrm{C}$$ room. If the mug is thermally insulated except for the top surface, what will be the final equilibrium temperature after a long time?

Accepted Answer

The coffee will eventually reach $$20^\circ\mathrm{C}$$, the temperature of the room.

Question 6

A polar bear weighing $$500\ \mathrm{kg}$$ stands on a sheet of ice that is $$0.5\ \mathrm{m}$$ thick. If the density of ice is $$900\ \mathrm{kg/m^3$}$$, what is the minimum area of ice needed to support the bear without sinking? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$A = \dfrac{mg}{ho_{ice} \cdot g \cdot d} = \dfrac{500}{900 	imes 0.5} = 1.11\ \mathrm{m^2$}$$

Question 7

A weather balloon is released at $$10^\circ\mathrm{C}$$ and rises to an altitude where the temperature is $$-20^\circ\mathrm{C}. $$Assuming the pressure remains constant and the balloon contains $$1.0$$ mole of gas, by what factor does the volume change? (Use $$PV = nRT)$$

Accepted Answer

The volume decreases by a factor of $$\dfrac{253}{283}.$$

Question 8

A water tower is open to the atmosphere at the top and connected to a pipe at the bottom. If the height difference between the water surface and the pipe outlet is $$15\ \mathrm{m}$$, what is the pressure difference between the top and the bottom of the tower? (Density of water $$= 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta P = ho g h = 1000 	imes 9.8 	imes 15 = 147,000\ \mathrm{Pa}$$

Question 9

An airplane wing is designed so that air flows faster over the top than the bottom. According to Bernoulli's equation, what is the effect on the pressure above the wing?

Accepted Answer

The pressure above the wing is lower than below the wing.

Question 10

A mass attached to a spring oscillates with amplitude $$A$$ and spring constant $$k. $$What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m}{k}}$$

Question 11

Which of the following best describes the difference between the propagation speed of a wave on water and the oscillation of water particles?

Accepted Answer

The propagation speed is the speed at which the wave travels, while the oscillation speed is the speed of the water particles moving up and down.

Question 12

A $$0.5\ \mathrm{kg}$$ mass is attached to a spring with $$k = 200\ \mathrm{N/m}. $$What is the maximum velocity if the amplitude is $$0.1\ \mathrm{m}$$?

Accepted Answer

$$v_{max} = A \sqrt{\dfrac{k}{m}} = 0.1 	imes \sqrt{\dfrac{200}{0.5}} = 2\ \mathrm{m/s}$$

Question 13

A hydraulic lift uses oil with a density of $$850\ \mathrm{kg/m^3$}. If $$the height difference between two pistons is $$2\ \mathrm{m}$$, what is the pressure difference between the pistons? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta P = ho g h = 850 	imes 9.8 	imes 2 = 16,660\ \mathrm{Pa}$$

Question 14

Which of the following best defines heat in the context of physics?

Accepted Answer

Heat is the energy transferred between objects due to a temperature difference.

Question 15

A $$2\ \mathrm{kg}$$ object falls from a height of $$10\ \mathrm{m}$$ and lands with a speed of $$12\ \mathrm{m/s}. $$What is the total mechanical energy just before impact? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$E = mgh + \dfrac{1}{2}mv^2$ = 2 	imes 9.8 	imes 10 + 0.5 	imes 2 	imes 12^2$ = 196 + 144 = 340\ \mathrm{J}$$

Question 16

For a string fixed at both ends, the allowed wavelengths are given by $$\lambda_n = \dfrac{2L}{n}$$, where $$n = 1, 2, 3, \ldots. $$What does $$n$$ represent?

Accepted Answer

$$n is $$the harmonic number, representing the mode of vibration.

Question 17

A fishing rod is thrown into the ocean and the bait at the end moves up and down with the waves. What type of motion does the bait experience?

Accepted Answer

Simple harmonic motion.

Question 18

In simple harmonic motion, when is the potential energy of the system at its maximum?

Accepted Answer

When the object is at maximum displacement (amplitude).

Question 19

The root mean square (RMS) speed of gas molecules is given by $$v_{rms} = \sqrt{\dfrac{3kT}{m}}. $$What does $$k$$ represent in this equation?

Accepted Answer

$$k is $$the Boltzmann constant.

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