Q: The surface of the water in a storage tank is $$30\ \text{m}$$ above a water faucet in the kitchen of a house. Calculate the difference in water pressure between the faucet and the surface of the water in the tank.

$$\Delta P = \rho g h = 1000 \cdot 9.8 \cdot 30 = 294,000\ \text{Pa}$$

Q: A 0.25kg mass at the end of a spring oscillates 2.2 times per second with an amplitude of 0.15m. What is the speed when it passes the equilibrium point?

$$v_{max} = 2\pi f A = 2\pi \cdot 2.2 \cdot 0.15 = 2.07\ \text{m/s}$$

Q: A sound wave in air has a frequency of $$282\ \text{Hz}$$ and travels with a speed of $$343\ \text{m/s}. $$How far apart are the wave crests (compressions)?

$$\lambda = \frac{v}{f} = \frac{343}{282} = 1.22\ \text{m}$$

Q: A 3kg cylinder of solid iron is supported by a spring while submerged in water. The density of iron is $$7860\ \text{kg/m}^3$$ and that of water is $$1000\ \text{kg/m}^3. $$What is the tension in the string?

$$T = mg - \rho_{water} V g = 11\ \text{N}$$

Question 1

A uniform beam of length $$2.20\ 	ext{m}$$ and mass $$25\ 	ext{kg} is $$mounted by a hinge on a wall and held horizontally by a cable making an angle $$	heta = 30^\circ$$ with the beam. The beam supports a sign of mass $$28\ 	ext{kg}$$ suspended from its end. What is the tension $$F_T in $$the supporting cable?

Accepted Answer

$$F_T = \frac{(mg \cdot \frac{L}{2} + Mg \cdot L)}{L \cdot \sin	heta}$$

Question 2

Refer to the diagram of three identical balls suspended from a ceiling on pairs of ropes. Which case has the greatest sum of the vertical components of the forces of tension?

Accepted Answer

All have the same magnitude of vertical components of forces of tension

Question 3

In the mobile shown, horizontal bars are massless and extend four times as far to the right than to the left. If toy #4 (yellow) has a mass of $$10\ 	ext{g}$$, what should the mass of toy #2 be to balance the mobile?

Accepted Answer

Question 4

A 15kg child is sitting on a playground seesaw board, 1.5m from the pivot. What is the minimum distance on the other side of the pivot, such that a 180N force will balance the seesaw board?

Accepted Answer

$$1.7\ 	ext{m}$$

Question 5

Water flows through a $$1\ 	ext{cm}$$ diameter pipe connected to a $$0.5\ 	ext{cm}$$ diameter pipe. Compared to the speed of the water in the $$0.5\ 	ext{cm}$$ pipe, the speed in the $$1\ 	ext{cm}$$ pipe is:

Accepted Answer

$$\frac{1}{4}$$

Question 6

The surface of the water in a storage tank is $$30\ 	ext{m}$$ above a water faucet in the kitchen of a house. Calculate the difference in water pressure between the faucet and the surface of the water in the tank.

Accepted Answer

$$\Delta P = ho g h = 1000 \cdot 9.8 \cdot 30 = 294,000\ 	ext{Pa}$$

Question 7

Water and then oil are poured into a U-shaped tube, open at both ends. They come to equilibrium. If the height of the water column is $$27.2\ 	ext{cm}$$ and the oil column is $$8.62\ 	ext{cm}$$, what is the density of the oil?

Accepted Answer

$$\rho_{oil} = \rho_{water} \cdot \frac{h_{oil}}{h_{water}} = 1000 \cdot \frac{8.62}{27.2}$$

Question 8

A 0.25kg mass at the end of a spring oscillates 2.2 times per second with an amplitude of 0.15m. What is the speed when it passes the equilibrium point?

Accepted Answer

$$v_{max} = 2\pi f A = 2\pi \cdot 2.2 \cdot 0.15 = 2.07\ 	ext{m/s}$$

Question 9

A sound wave in air has a frequency of $$282\ 	ext{Hz}$$ and travels with a speed of $$343\ 	ext{m/s}. $$How far apart are the wave crests (compressions)?

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{343}{282} = 1.22\ 	ext{m}$$

Question 10

A 5000Hz sound wave is emitted by a stationary source and reflects from an object moving $$3.5\ 	ext{m/s}$$ toward the source. What is the frequency of the wave reflected by the moving object as detected by a detector at rest near the source? (Speed of sound at $$4^\circC is$$ $$343\ 	ext{m/s})$$

Accepted Answer

$$f'' = f' / \left(1 - \frac{v_{src}}{v_{snd}}\right)$$

Question 11

A 60kg woman stands on the very end of a uniform board, of length $$l$$, which is supported one-quarter of the way from one end and is balanced. What is the mass of the board?

Accepted Answer

$$120\ 	ext{kg}$$

Question 12

A 3kg cylinder of solid iron is supported by a spring while submerged in water. The density of iron is $$7860\ 	ext{kg/m}^3$$ and that of water is $$1000\ 	ext{kg/m}^3. $$What is the tension in the string?

Accepted Answer

$$T = mg - ho_{water} V g = 11\ 	ext{N}$$

Question 13

Pendulum A has a length $$L$$ and pendulum B has a length $$L/4. $$How do their periods compare?

Accepted Answer

Period of B is $$\frac{1}{2}$$ that of A

Question 14

What is the relationship between frequency and wavelength considering a moving ambulance moving towards an observer (Doppler Effect)?

Accepted Answer

Higher frequency, shorter wavelength

Question 15

What is Avogadro’s number ($$N_A$$)?

Accepted Answer

$$N_A = 6.02 	imes 10$$^{23}$$

Question 16

What is Boltzmann’s constant ($$k$$)?

Accepted Answer

$$k = 1.38 	imes 10$$^{-23}$$\ 	ext{J/K}$$

Question 17

Oxygen and hydrogen are kept under the same temperature and pressure. The oxygen molecule has a 16 times greater mass than the hydrogen molecule. What can be predicted about the average kinetic energy of the oxygen molecule?

Accepted Answer

Same as hydrogen

Question 18

If the pressure in a gas is tripled while its volume is held constant, by what factor does $$v_{rms}$$ change?

Accepted Answer

$$v_{rms}$$ increases by $$\sqrt{3}$$

Static Equilibrium: Beam Supported by Cable and Hinge

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