3.90 x 10^{5} gallons of tar (SG = 1.20) is stored in a 23.0-ft tall storage tank.

What is the total mass of the liquid in the tank?

What is the pressure at the bottom of the tank?

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Suppose the vessel containing the water and the ice is full: The water level is at the vessel’s rim. What happens once the ice melts?

A. The water overflows.

B. The level of the water remains at the rim.

C. There is not enough information given, the outcome is not definite.

D. The level of the water drops below the rim.

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Consider a rectangular block of ice floating in water in an open vessel. Let * a* denote the height of the ice block showing above the water surface, and

Given * a*,

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Two objects of masses 28 kg and 21 kg are hung from the ends of a stick that is 70 cm long and has marks every 10 cm, as shown.

If the mass of the stick is negligible, at which of the points indicated should a cord be attached if the stick is to remain horizontal when suspended from the cord?

1. B

2. D

3. G

4. F

5. C

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A simple harmonic oscillator consists of a mass on a horizontal spring, oscillating with an amplitude A and negligible friction. What is the distance of the mass to the equilibrium position (x = 0) at the instant when the kinetic and potential energies are equal?

i. 0

ii. A

iii. A/√ 2

iv. A/2

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When a tuning fork of frequency 565 Hz vibrates beside a piano string, beats are heard. The string is loosened slightly and the beats go away. What was the original frequency of the string?

A. 565 Hz

B. greater than 565 Hz

C. less than 565 Hz

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A police car is traveling at a speed *v _{c}* to the right and a truck is traveling at a speed

What is the frequency *f _{t}* heard by an observer in the moving truck? Let

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Suppose that a volleyball A and a bowling ball B are completely submerged in water and have the same volume, as in the figure. (Of course, you would have to hold the volleyball beneath the water to keep it from popping up to the surface.)

Which feels a greater buoyant force?

A. bowling ball B

B. Unable to determine

C. They feel the same buoyant force.

D. volleyball A

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If a liquid only half as dense as mercury were used in a barometer, how high would its level be on a day of normal atmospheric pressure (when the mercury barometer reads 76 cm)?

A. 152 cm

B. 76 cm

C. 19 cm

D. 304 cm

E. 38 cm

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A spring with spring constant *k* oscillates with a total mass *m*. The shortest time interval between the instant of greatest speed and the instant when it turns around is

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A string is stretched to a length *ℓ* and both ends are fixed. The density of the string is µ and its tension is* F*. A standing wave mode of the string with six nodes, including both end points (as pictured), is generated.

What is the frequency of this oscillation?

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An organ pipe of length *L* is open at one end and closed at the other. A tuning fork is brought near the pipe, exciting the air in the pipe with three nodes as represented in the figure.

With the speed of the sound denoted by *v*, what is the frequency of the tuning fork?

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A group of swimmers is resting in the sun on an off-shore raft. They estimate that 2.79 m separate a trough and an adjacent crest of surface waves on the lake. They count 14 crests that pass by the raft in 20.7 s. How fast are the waves moving?

A. 3.88251

B. 4.75641

C. 4.55385

D. 4.17228

E. 3.72

F. 3.77391

G. 5.43646

H. 4.01154

I. 3.30603

J. 5.30653

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A thin uniform cylindrical turntable of radius 3 m and mass 25 kg rotates in a horizontal plane with an initial angular speed of 7.9 rad/s. The turntable bearing is frictionless. A clump of clay of mass 12 kg is dropped onto the turntable and sticks at a point 1.1 m from the point of rotation.

Find the angular speed of the clay and turntable.

A. 7.75532

B. 5.75699

C. 6.99693

D. 11.0707

E. 7.097

F. 8.15289

G. 8.35556

H. 4.96894

I. 8.6087

J. 9.56476

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A simple harmonic oscillator has amplitude 0.72 m and period 2.2 sec. What is the maximum acceleration?

A. 0.934689 m/s^{2}

B. 0.327273 m/s^{2}

C. 5.87282 m/s^{2}

D. 0.14876 m/s^{2}

E. 12.9202 m/s^{2}

F. 2.93641 m/s^{2}

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A simple pendulum has a period of 2.74 s on the surface of the Earth where the acceleration of gravity is 9.8 m/s^{2} . What would be its period on the Moon, where the acceleration of gravity is 1.67 m/s^{2} ?

A. 9.08419

B. 8.4059

C. 3.51255

D. 5.88655

E. 2.97961

F. 5.30517

G. 6.63751

H. 3.29453

I. 6.51639

J. 2.83427

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A non-uniform beam with a mass 3 *M* and length *L* is in stable equilibrium when placed at the edge of a table with half its length sticking off the table edge. But when a pointlike mass *M* is placed at the far end of the part of the beam off the table, the beam is brought to unstable equilibrium; i.e., it is right on the verge of tipping off the table.

At what distance to the left of the table edge is the center of mass of the beam located?

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A block of density *ρ _{1}* and volume

Find *V _{2}* such that the two blocks are just submerged, as shown in figure above.

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The displacement in simple harmonic motion is a maximum when

A. acceleration is zero.

B. potential energy is maximum.

C. kinetic energy is maximum.

D. potential energy is zero.

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An incompressible fluid is flowing through a horizontal tube which, at some point has a constriction such that the area of the tube becomes much smaller.

How do the fluid pressure and speed of flow compare at point B in the constricted region to their values at point A in the normal part of the tube?

A. The pressure and speed of flow are both much greater at point A than at point B.

B. The pressure and speed of flow are both much greater at point B than at point A.

C. At point B, the speed of flow is less but the pressure is greater than at point A.

D. Because the fluid is incompressible, the pressure and speed of flow must be constant throughout the tube.

E. At point A, the speed of flow is less but the pressure is greater than at point B.

Watch Solution

Cats can hear sound frequencies up to 70,000 Hz. Bats send and receive ultrahigh frequency squeaks up to 120,000 Hz. Which hears the sound of shorter wavelengths?

A. cats

B. Neither; the wavelength is independent of frequency.

C. bats

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A simple U-tube that is open at both ends is partially filled with a heavy liquid of density 1000 kg/m^{3} . A liquid of density 568 kg/m^{3} is then poured into one arm of the tube, forming a column 12 cm in height, as shown.

What is the difference in the heights of the two liquid surfaces?

A. 5.54

B. 1.8582

C. 1.7507

D. 1.0318

E. 2.4066

F. 5.184

G. 9.288

H. 3.3512

I. 2.954

J. 5.97

Watch Solution

A simple pendulum has a period of *T* on the surface of the Earth. If the same pendulum were brought to the surface of a planet where the acceleration due to gravity is 4 times greater than that on the Earth, its period would

A. decrease by a factor of 16

B. decrease by a factor of 2

C. remain the same

D. decrease by a factor of 4

E. increase by a factor of 16

F. increase by a factor of 4

G. increase by a factor of 2

Watch Solution

A beaker of mass 1 kg containing 2.5 kg of water rests on a scale. A 3.1 kg block of a metallic alloy of density 4900 kg/m^{3} is suspended from a spring scale and is submerged in the water of density 1000 kg/m^{3} as shown in the figure.

What does the hanging scale read? The acceleration due to gravity is 9.8 m/s ^{2}.

A. 21.3715

B. 16.043

C. 23.0577

D. 28.3774

E. 14.3733

F. 31.6615

G. 27.8826

H. 24.18

I. 23.8994

J. 27.6033

Watch Solution

A 39.3 g mass is attached to a horizontal spring with a spring constant of 8.62 N/m and released from rest with an amplitude of 34.6 cm.

What is the speed of the mass when it is halfway to the equilibrium position if the surface is frictionless?

A. 2.93522

B. 5.80081

C. 3.41751

D. 2.26646

E. 9.3472

F. 4.23824

G. 2.7086

H. 4.7789

I. 4.43776

J. 2.64816

Watch Solution