Q: A wheel of radius $$0.40\ \text{m} is $$mounted on frictionless bearings. A block is suspended from a rope wound around the wheel and descends $$1.5\ \text{m} in$$ $$2.00\ \text{s}$$ without slipping. The tension in the rope during descent is $$20\ \text{N}. $$What is the moment of inertia of the wheel?

4.3\ \text{kg} \cdot \text{m}^2

Q: A cold trap with a volume of $$0.200\ \text{L} is $$maintained at $$13.0\ \text{K}$$ and $$10.0\ \text{Pa}$$ pressure. How many molecules are in it? (Avogadro's number $$6.022 \times 10$$^{23}$$, universal gas constant 8.314$$\ \text{J/(mol} \cdot \text{K)}$$)

$$1.11 \times 10$$^{19}$$ molecules

Question 1

A horizontal force $$\vec{F} of 30.0 N $$pushes two blocks, A and B, to the right on a horizontal surface. Block A has mass $$m_A = 3.00\ 	ext{kg}$$ and block B has mass $$m_B = 2.00\ 	ext{kg}. $$The coefficient of kinetic friction between the blocks and the floor is $$\mu_k = 0.2. $$What is the magnitude of the force that block A exerts on block B?

Accepted Answer

12.0 N

Question 2

A wheel of radius $$0.40\ 	ext{m} is $$mounted on frictionless bearings. A block is suspended from a rope wound around the wheel and descends $$1.5\ 	ext{m} in$$ $$2.00\ 	ext{s}$$ without slipping. The tension in the rope during descent is $$20\ 	ext{N}. $$What is the moment of inertia of the wheel?

Accepted Answer

4.3\ 	ext{kg} \cdot 	ext{m}^2

Question 3

A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall, forming a $$53^\circ$$ angle above the horizontal. The coefficient of static friction between the floor and the ladder is $$0.28. $$What distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip?

Accepted Answer

1.73\ 	ext{m}

Question 4

Two water reservoirs are open to the atmosphere and connected by a manometer containing mercury ($$ho_{Hg} = 13,600\ 	ext{kg/m}^3). $$The manometer reading is $$m = 25.0\ 	ext{cm}. If $$the water density is $$1000\ 	ext{kg/m}^3$$, what is the difference in elevation $$h$$ between the reservoirs?

Accepted Answer

3.15\ 	ext{m}

Question 5

A paint sprayer pumps air through a constriction in a $$2.50\ 	ext{cm}$$ diameter pipe. The air speed in the $$2.50\ 	ext{cm}$$ section is $$5.00\ 	ext{m/s}. $$The density of air is $$1.29\ 	ext{kg/m}^3$$, and the density of paint is $$1200\ 	ext{kg/m}^3. $$What is the maximum diameter of the constriction that will allow the sprayer to operate?

Accepted Answer

8.07\ 	ext{mm}

Question 6

The figure shows the displacement $$y of a $$traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

Accepted Answer

0.75\ 	ext{m/s}

Question 7

A 2.0-m long string is fixed at both ends and tightened until the wave speed is $$160\ 	ext{m/s}. $$What is the frequency of the standing wave if, not counting the two fixed ends, there are three nodes along the string?

Accepted Answer

160\ 	ext{Hz}

Question 8

The saturated vapor pressure for water at $$20^\circ	ext{C} is$$ $$2.33 	imes 10^3$\ 	ext{Pa}. On a $$cold winter day, the outside temperature is $$0^\circ	ext{C}$$ with a relative humidity of $$60\%. $$The heater draws cold air from outside and heats it to $$20^\circ	ext{C}$$, drying the air. How much water must evaporate to raise the humidity of a $$30\ 	ext{m}^3$$ bedroom to $$40\%$$? (Molar mass of water is $$18\ 	ext{g/mol})$$

Accepted Answer

125\ 	ext{g}

Question 9

A Carnot cycle engine operates between a low temperature reservoir at $$20^\circ	ext{C}$$ and a high temperature reservoir at $$800^\circ	ext{C}. If $$the engine outputs $$20.0\ 	ext{kJ} of $$work per cycle, how much heat must the high temperature reservoir transfer to the engine during each cycle?

Accepted Answer

39.2\ 	ext{kJ}

Question 10

A blacksmith heats a steel plate measuring $$10\ 	ext{cm} 	imes 15\ 	ext{cm} 	imes 1\ 	ext{mm} to$$ $$600^\circ	ext{C}. If $$the emissivity is $$0.75$$, what is the total rate at which it radiates energy? (Stefan-Boltzmann constant $$\sigma = 5.670 	imes 10$$^{-8}$$\ 	ext{W/m}^2 \cdot 	ext{K}^4)$$

Accepted Answer

741\ 	ext{W}

Question 11

A substance has a melting point of $$20^\circ	ext{C}$$ and a latent heat of fusion of $$3.5 	imes 10^4$\ 	ext{J/kg}. $$The boiling point is $$150^\circ	ext{C}$$ and the latent heat of vaporization is $$7.0 	imes 10^4$\ 	ext{J/kg}. $$The specific heats for the solid, liquid, and gaseous phases are $$600\ 	ext{J/(kg} \cdot 	ext{K)}$$, $$1000\ 	ext{J/(kg} \cdot 	ext{K)}$$, and $$400\ 	ext{J/(kg} \cdot 	ext{K)}$$, respectively. What is the quantity of heat given up by $$0.50\ 	ext{kg} of $$the substance when cooled from $$170^\circ	ext{C} to$$ $$88^\circ	ext{C}$$?

Accepted Answer

70\ 	ext{kJ}

Question 12

A cold trap with a volume of $$0.200\ 	ext{L} is $$maintained at $$13.0\ 	ext{K}$$ and $$10.0\ 	ext{Pa}$$ pressure. How many molecules are in it? (Avogadro's number $$6.022 	imes 10$$^{23}$$, universal gas constant 8.314$$\ 	ext{J/(mol} \cdot 	ext{K)}$$)

Accepted Answer

$$1.11 	imes 10$$^{19}$$ molecules

Question 13

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?

Accepted Answer

4.5\ 	ext{Hz}

Question 14

A person hears two sound waves simultaneously. One has a period of $$1.50\ 	ext{ms}$$ and the other $$1.51\ 	ext{ms}. $$What is the beat frequency?

Accepted Answer

4.4\ 	ext{Hz}

Question 15

You are standing on the side of the road when you hear the siren of a police car approaching you from behind and perceive the frequency as $$1358\ 	ext{Hz}. $$Once the police car has passed, you perceive the frequency as $$1075\ 	ext{Hz}. $$What is the speed of the police car? (Speed of sound in air is $$343\ 	ext{m/s})$$

Accepted Answer

40.0\ 	ext{m/s}

Question 16

The solar constant representing sunlight intensity on Earth is $$1350\ 	ext{W/m}^2. If $$sunlight is emitted isotropically from the Sun, what is the sunlight intensity on Mars? (Average distance from Sun to Earth: $$1.49 	imes 10^8$\ 	ext{km}$$, Sun to Mars: $$2.29 	imes 10^8$\ 	ext{km})$$

Accepted Answer

571\ 	ext{W/m}^2

Question 17

A box of mass $$m is $$pressed against an ideal spring of force constant $$k$$, compressing the spring a distance $$x. $$After release, the box slides up a frictionless incline and stops. If the spring is compressed a distance $$2x$$, how high will the box go up the incline compared to before?

Accepted Answer

Four times higher

Question 18

When a fixed amount of ideal gas goes through an isothermal expansion, which statement is correct?

Accepted Answer

Its internal (thermal) energy does not change.

Question 19

An ice cube at $$0^\circ	ext{C} is $$placed in a large bathtub filled with water at $$30^\circ	ext{C}$$ and allowed to melt, causing no appreciable change in the bath water temperature. Which statement is true?

Accepted Answer

The entropy of the system (ice plus water) increases because the process is irreversible.

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