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Physic
Q:
Two identical undamped oscillators have the same amplitude of oscillation only if:
A) they are started with the same displacement x0
B) they are started with the same velocity v0
C) they are started with the same phase
D) they are started so the combination is the same
E) they are started so the combination is the same
Q:
In simple harmonic motion, the displacement is maximum when the:
A) acceleration is zero
B) velocity is maximum
C) velocity is zero
D) kinetic energy is maximum
E) momentum is maximum
Q:
The amplitude and phase constant of an oscillator are determined by:
A) the frequency
B) the angular frequency
C) the initial displacement alone
D) the initial velocity alone
E) both the initial displacement and velocity
Q:
This plot shows a mass oscillating as x= xmcos (ωt+ φ). What are xmand φ? A) 1 m, 0
B) 2 m, 0
C) 2 m, 90
D) 4 m, 0
E) 4 m, 90
Q:
A block attached to a spring oscillates in simple harmonic motion along the xaxis. The limits of its motion are x= 10 cm and x= 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are:
A) 40 cm, 2 Hz
B) 20 cm, 4 Hz
C) 40 cm, 4 Hz
D) 25 cm, 4 Hz
E) 20 cm, 2 Hz
Q:
Frequency f and angular frequency ï·are related by
Q:
An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its angular frequency is:
A) 0.79 rad/s
B) 1.57 rad/s
C) 2.0 rad/s
D) 6.3 rad/s
E) 12.6 rad/s
Q:
An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its frequency is:
A) 2 Hz
B) 10 s
C) 0.05 Hz
D) 2 s
E) 0.50 s
Q:
An object attached to one end of a spring makes 20 complete vibrations in 10s. Its period is:
A) 2 Hz
B) 10 s
C) 0.5 Hz
D) 2 s
E) 0.50 s
Q:
A particle is in simple harmonic motion with period T. At time t=0 it is halfway between the equilibrium point and an end point of its motion, travelling toward the end point. The next time it is at the same place is:
A) t= T
B) t= T/2
C) t= T/3
D) t= T/4
E) none of the above
Q:
A particle moves back and forth along the xaxis from x= -xmto x= +xm, in simple harmonic motion with period T.At time t= 0 it is at x= +xm. When t= 0.75T:A) it is at x= 0 and is traveling toward x= +xmB) it is at x= 0 and is traveling toward x= -xmC) it is at x= +xmand is at restD) it is between x= 0 and x= +xmand is traveling toward x= -xmE) it is between x= 0 and x= -xmand is traveling toward x= -xm
Q:
A particle is in simple harmonic motion with period T.At time t= 0 it is at the equilibrium point. At the times listed below it is at various points in its cycle. Which of them is farthest away from the equilibrium point?
A) 0.5T
B) 0.7T
C) T
D) 1.4T
E) 1.5T
Q:
An oscillatory motion must be simple harmonic if:
A) the amplitude is small
B) the potential energy is equal to the kinetic energy
C) the motion is along the arc of a circle
D) the acceleration varies sinusoidally with time
E) the derivative, dU/dx, of the potential energy is negative
Q:
It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:
A) masses
B) periods
C) amplitudes
D) spring constants
E) kinetic energies
Q:
A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:
A) T
B) 1.5 T
C) 2T
D) T/2
E) 4T
Q:
When a body executes simple harmonic motion, its acceleration at the ends of its path must be:
A) zero
B) less than g
C) more than g
D) suddenly changing in sign
E) none of these
Q:
An object is undergoing simple harmonic motion. Throughout a complete cycle it:
A) has constant speed
B) has varying amplitude
C) has varying period
D) has varying acceleration
E) has varying mass
Q:
A particle oscillating in simple harmonic motion is:
A) never in equilibrium because it is in motion
B) never in equilibrium because there is a force
C) in equilibrium at the ends of its path because its velocity is zero there
D) in equilibrium at the center of its path because the acceleration is zero there
E) in equilibrium at the ends of its path because the acceleration is zero there
Q:
A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be:
A) half the natural frequency of the oscillator
B) the same as the natural frequency of the oscillator
C) twice the natural frequency of the oscillator
D) unrelated to the natural frequency of the oscillator
E) determined from the maximum speed desired
Q:
A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by:
A) the damping force
B) the initial amplitude
C) the initial velocity
D) the force of gravity
E) none of the above
Q:
An oscillator is driven by a sinusoidal force. The frequency of the applied force:
A) must be equal to the natural frequency of the oscillator
B) becomes the natural frequency of the oscillator
C) must be less than the natural frequency of the oscillator
D) must be greater than the natural frequency of the oscillator
E) is independent of the natural frequency of the oscillator
Q:
A block on a spring is subjected to an applied sinusoidal force AND to a damping force that is proportional to its velocity. The energy dissipated by damping is supplied by:
A) the potential energy of the spring
B) the kinetic energy of the mass
C) gravity
D) friction
E) the applied force
Q:
An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time:
A) its amplitude is an increasing function of time
B) its amplitude is a decreasing function of time
C) its amplitude is constant
D) its amplitude is a decreasing function of time only if the damping constant is large
E) its amplitude increases over some portions of a cycle and decreases over other portions
Q:
Below are sets of values for the spring constant k, damping constant b, and mass mfor a particle in damped harmonic motion. Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?
k b m
A) k0 b0 m0
B) 3k0 2b0 m0
C) k0/2 6b0 2m0
D) 4k0 b0 2m0
E) k0 b0 10m0
Q:
Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass mare given below. Which leads to the smallest rate of loss of mechanical energy?
A) k= 100N/m, m= 50g, b= 8gm/s
B) k= 150N/m, m= 50g, b= 5gm/s
C) k= 150N/m, m= 10g, b= 8gm/s
D) k= 200N/m, m= 8g, b= 6gm/s
E) k= 100N/m, m= 2g, b= 4gm/s
Q:
A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3kgm/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x= 1.5 m, at time t= 0, what is the angular frequency of the oscillations?
A) 4.0 rad/s
B) 8.0 rad/s
C) 12 rad/s
D) 23 rad/s
E) 45 rad/s
Q:
A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3kgm/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x= 1.5 m, at time t= 0, what is the amplitude of the motion at t= 5.0 s?
A) 1.5 m
B) 1.3 m
C) 1.0 m
D) 0.67 m
E) 0.24 m
Q:
A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3kgm/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x= 1.5 m, at time t= 0, what is the particle's position at t= 5.0 s?
A) -1.5 m
B) -0.73 m
C) 0 m
D) 0.73 m
E) 1.5 m
Q:
For an oscillator subjected to a damping force proportional to its velocity:
A) the displacement is a sinusoidal function of time
B) the velocity is a sinusoidal function of time
C) the frequency is a decreasing function of time
D) the mechanical energy is constant
E) none of the above is true
Q:
Both the xand ycoordinates of a point execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be:
A) an ellipse
B) a circle
C) a parabola
D) a hyperbola
E) a square
Q:
Both the xand ycoordinates of a point execute simple harmonic motion. The result might be a circular orbit if:
A) the amplitudes are the same but the frequencies are different
B) the amplitudes and frequencies are both the same
C) the amplitudes and frequencies are both different
D) the phase constants are the same but the amplitudes are different
E) the amplitudes and the phase constants are both different
Q:
The rotational inertia of a uniform thin rod about its end is ML2/3, where Mis the mass and Lis the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L= 1.0 m this rod will have the same period as a simple pendulum of length:
A) 33 cm
B) 50 cm
C) 67 cm
D) 100 cm
E) 150 cm
Q:
Bernoulli's equation can be derived from the conservation of:
A) energy
B) mass
C) angular momentum
D) volume
E) pressure
Q:
A non-viscous incompressible fluid is pumped steadily up a vertical pipe with uniform cross section. The difference in pressure between points at the top and bottom:
A) is the same as it would be if the fluid were motionless
B) is greater at higher flow rates than at lower flow rates
C) is less at higher flow rates than at lower flow rates
D) does not depend on the density of the fluid
E) is zero
Q:
Water is pumped into one end of a long pipe at the rate of 40 L/min. It emerges at the other end at 24 L/min. A possible reason for this decrease in flow is:
A) the water is being pumped uphill
B) the water is being pumped downhill
C) the diameter of the pipe is not the same at the two ends
D) friction in the pipe
E) a leak in the pipe
Q:
A non-viscous incompressible fluid is pumped steadily into the narrow end of a long tapered pipe and emerges from the wide end. The pressure at the input is greater than at the output. A possible explanation is:
A) the fluid speed increases from input to output
B) the fluid speed is the same at the two ends
C) the fluid is flowing uphill
D) the fluid is flowing downhill
E) the fluid is flowing horizontally
Q:
A non-viscous incompressible liquid is flowing through a horizontal pipe of constant cross-section. Bernoulli's equation and the equation of continuity predict that the drop in pressure along the pipe:
A) is zero
B) depends on the length of the pipe
C) depends on the fluid velocity
D) depends on the cross-sectional area of the pipe
E) depends on the height of the pipe
Q:
Water is pumped through the hose shown below, from a lower level to an upper level. Compared to the water at point 1, the water at point 2: A) has greater speed and greater pressure
B) has greater speed and less pressure
C) has less speed and less pressure
D) has less speed and greater pressure
E) has greater speed and the same pressure
Q:
Water flows through a constriction in a horizontal pipe. As it enters the constriction, the water's:
A) speed increases and pressure decreases
B) speed increases and pressure remains constant
C) speed increases and pressure increases
D) speed decreases and pressure increases
E) speed decreases and pressure decreases
Q:
A person blows across the top of one arm of a U-tube partially filled with water. The water in that arm:
A) rises slightly
B) drops slightly
C) remains at the same height
D) rises if the blowing is soft but drops if it is hard
E) rises if the blowing is hard but drops if it is soft
Q:
A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 x103kg/m3. The pressure in the main line is 2.0 x105Pa; then the difference in pressure between the main line and the second floor is:A) 6.9x104Pa with the main line at the higher pressureB) 2.3x104Pa with the main line at the higher pressureC) 6.9x104Pa with the main line at the lower pressureD) 2.3x104Pa with the main line at the lower pressureE) 9.1x104Pa with the main line at the higher pressure
Q:
A large tank filled with water has two holes in the bottom, one with twice the radius of the other. In steady flow the speed of water leaving the larger hole is ________ the speed of the water leaving the smaller.
A) twice
B) four times
C) half
D) one-fourth
E) the same as
Q:
A large water tank, open at the top, has a small hole in the bottom. When the water level is 30 m above the bottom of the tank, the speed of the water leaking from the hole:
A) is 2.5 m/s
B) is 24 m/s
C) is 44 m/s
D) cannot be calculated unless the area of the hole is given
E) cannot be calculated unless the areas of the hole and tank are given
Q:
Water (density = 1.0 x103kg/m3) flows through a horizontal tapered pipe. At the wide end its speed is 4.0 m/s. The difference in pressure between the two ends is 4.5 x103Pa. The speed of the water at the narrow end is:A) 2.6 m/sB) 3.2 m/sC) 4.0 m/sD) 4.5 m/sE) 5.0 m/s
Q:
Water (density = 1.0 x103kg/m3) flows downhill through a pipe of diameter 1.5 cm. Its speed at the top of the hill is 7.2 m/s. If the hill is 9.5 m high, what is the gravitational potential energy density of the water at the top of the hill relative to the bottom?A) cannot be calculated without knowing the pressureB) 120 J/m3C) 7.2 x 103J/m3D) 9.5 x 103J/m3E) 9.3 x 104J/m3
Q:
The units of pressure can also be written as:
A) N/m
B) Jm2
C) W/m2
D) J/m3
E) N/m3
Q:
A fluid of density 9.1 x102kg/m3is flowing through a tube at a speed of 5.3 m/s. What is the kinetic energy density of the fluid?A) cannot be calculated without knowing the pressureB) cannot be calculated without knowing the elevationC) 4.8 x103J/m3D) 1.3 x104J/m3E) 2.5x106J/m3
Q:
Consider a pipe containing a fluid, with the fluid being at rest. To apply Bernoulli's equation to this situation:
A) set vequal to zero because there is no motion
B) set gequal to zero because there is no acceleration
C) set vand gboth equal to zero
D) set pequal to the atmospheric pressure
E) cannot be done, Bernoulli's equation applies only to fluids in motion
Q:
The quantity yappearing in Bernoulli's equation MUST be measured:
A) upward from the center of the Earth
B) upward from the surface of the Earth
C) upward from the lowest point in the flow
D) downward from the highest point in the flow
E) upward from any convenient level
Q:
Which of the following assumptions is NOT made in the derivation of Bernoulli's equation?
A) assume streamline flow
B) neglect viscosity
C) neglect friction
D) neglect gravity
E) neglect turbulence
Q:
One end of a cylindrical pipe has a radius of 1.5 cm. Water (density = 1.0 x103kg/m3) streams steadily out at 7.0 m/s. The rate at which mass is leaving the pipe is:A) 2.5 kg/sB) 4.9 kg/sC) 7.0 kg/sD) 48 kg/sE) 7.0 x103kg/s
Q:
The diagram shows a pipe of uniform cross section in which water is flowing. The directions of flow and the volume flow rates (in cm3/s) are shown for various portions of the pipe. The direction of flow and the volume flow rate in the portion marked A are:
Q:
One end of a cylindrical pipe has a radius of 1.5 cm. Water (density = 1.0 x103kg/m3) streams steadily out at 7.0 m/s. The volume flow rate is:A) 4.9x10-3m3/sB) 2.5 m3/sC) 4.9 m3/sD) 7.0 m3/sE) 48 m3/s
Q:
Water is streaming downward from a faucet opening with an area of 3.0 x10-5m2. It leaves the faucet with a speed of 5.0 m/s. The cross sectional area of the stream 0.50 m below the faucet is:A) 1.5 x10-5m2B) 2.0 x10-5m2C) 2.5 x10-5m2D) 3.0 x10-5m2E) 3.5 x10-5m2
Q:
A lawn sprinkler is made of a 1.0 cm diameter garden hose with one end closed and 25 holes, each with a diameter of 0.050 cm, cut near the closed end. If water flows at 2.0 m/s in the hose, the speed of the water leaving a hole is:
A) 2.0 m/s
B) 32 m/s
C) 40 m/s
D) 600 m/s
E) 800 m/s
Q:
Water flows from a 6.0-cm diameter pipe into an 8.0-cm diameter pipe. The speed in the 6.0-cm pipe is 5.0 m/s. The speed in the 8-inch pipe is:
A) 2.8 m/s
B) 3.8 m/s
C) 6.7 m/s
D) 8.9 m/s
E) 9.9 m/s
Q:
A constriction in a pipe reduces its diameter from 4.0 cm to 2.0 cm. Where the pipe is narrow the water speed is 8.0 m/s. Where it is wide the water speed is:
A) 2.0 m/s
B) 4.0 m/s
C) 8.0 m/s
D) 16 m/s
E) 32 m/s
Q:
Water flows through a cylindrical pipe of varying cross-section. The velocity is 3.0 m/s at a point where the pipe diameter is 1.0 cm. At a point where the pipe diameter is 3.0 cm, the velocity is:
A) 9 m/s
B) 3 m/s
C) 1 m/s
D) 0.33 m/s
E) 0.11 m/s
Q:
An incompressible liquid flows along the pipe as shown. The ratio of the speeds v2/v1is: A) A1/A2
B) A2/A1
C) D) E) v1/v2
Q:
Which of the following is true?
A) A streamline can only be defined for irrotational flow.
B) A streamline cannot be defined for turbulent flow.
C) Streamlines cannot cross in laminar flow, but can cross in turbulent flow.
D) A streamline is the path that a tiny element of fluid would take as the fluid flows.
E) The velocity vector of a fluid element is always perpendicular to the streamline.
Q:
A fluid is undergoing steady flow. Therefore:
A) the velocity of any given molecule of fluid does not change
B) the pressure does not vary from point to point
C) the velocity at any given point does not vary with time
D) the density does not vary from point to point
E) the flow is not uphill or downhill
Q:
A fluid is undergoing "incompressible" flow. This means that:
A) the pressure at a given point cannot change with time
B) the velocity at a given point cannot change with time
C) the velocity must be the same everywhere
D) the pressure must be the same everywhere
E) the density cannot change with time or location
Q:
The equation of continuity for fluid flow can be derived from the conservation of:
A) energy
B) mass
C) angular momentum
D) volume
E) pressure
Q:
A 0.50 N metal sinker appears (as measured using a spring scale) to have a mass of 0.45 N when submerged in water. The specific gravity of the metal is:
A) 6
B) 8
C) 9
D) 10
E) 12
Q:
The apparent weight of a steel sphere immersed in various liquids is measured using a spring scale. The greatest reading is obtained for that liquid:
A) having the smallest density
B) having the largest density
C) subject to the greatest atmospheric pressure
D) having the greatest volume
E) in which the sphere was submerged deepest
Q:
A steel ax and an aluminum piston have the same apparent weight in water. When they are weighed in air:
A) they weigh the same
B) the ax is heavier
C) the piston is heavier
D) both weigh less than they did in water
E) depends on their shapes
Q:
A 210-g object apparently loses 30 g when suspended in a liquid of density 2.0 g/cm3. The density of the object is:
A) 7.0 g/cm3
B) 3.5 g/cm3
C) 1.4 g/cm3
D) 14 g/cm3
E) none of these
Q:
A solid has a volume of 8 cm3. When weighed on a spring scale calibrated in grams, the scale indicates 20 g. What does the scale indicate if the object is weighed while immersed in a liquid of density 2 g/cm3?
A) 4 g
B) 10 g
C) 12 g
D) 16 g
E) zero, since the object will float
Q:
A tin can has a volume of 1000 cm3and a mass of 100 g. Approximately what mass of lead shot can it carry without sinking in water?
A) 900 g
B) 100 g
C) 1000 g
D) 1100 g
E) 980 g
Q:
The dimensions of a wooden raft (density = 150 kg/m3) are 3.0 m x3.0 m x1.0 m. What maximum load can it carry in sea water (density =1020 kg/m3)?A) 1350 kgB) 7800 kgC) 9200 kgD) 19,500 kgE) 24,300 kg
Q:
A rock, which weighs 1400 N in air, has an apparent weight of 900 N when submerged in fresh water (998 kg/m3). The volume of the rock is:A) 0.14 m3B) 0.50 m3C) 0.90 m3D) 5.1 x10-2m3E) 9.2 x10-2m3
Q:
An object hangs from a spring balance. The balance indicates 30 N in air, 20 N when the object is submerged in water. What does the balance indicate when the object is submerged in liquid with a density that is half of water?
A) 20 N
B) 25 N
C) 30 N
D) 35 N
E) 40 N
Q:
An object hangs from a spring balance. The balance indicates 30 N in air, 20 N when the object is submerged in water. Which of the following is true?
A) The actual weight of the object is 20 N.
B) The actual weight of the object is 10 N.
C) The actual weight of the object is slightly more than 30 N, due to the buoyant force of the air.
D) The actual weight of the object is slightly less than 30 N, due to the buoyant force of the air.
E) The actual weight of the object is equal to the apparent weight of the object in both cases.
Q:
A loaded ship passes from a lake (fresh water) to the ocean (salt water). Salt water is denser than fresh water and as a result the ship will:
A) ride higher in the water
B) settle lower in the water
C) ride at the same level in the water
D) experience an increase in buoyant force
E) experience a decrease in buoyant force
Q:
A boat floating in fresh water displaces 16,000 N of water. How many newtons of saltwater would it displace if it floats in saltwater of specific gravity 1.10?
A) 12,800 N
B) 14,400 N
C) 16,000 N
D) 17,600 N
E) 19,200 N
Q:
A wood board floats in fresh water with 60% of its volume under water. The density of the woodis:
A) 0.4 g/cm3
B) 0.5 g/cm3
C) 0.6 g/cm3
D) less than 0.4 g/cm3
E) more than 0.6 g/cm3
Q:
A student standardizes the concentration of a salt-water solution by slowly adding salt until an egg will just float. The procedure is based on the assumption that:
A) all eggs have the same volume
B) all eggs have the same weight
C) all eggs have the same density
D) all eggs have the same shape
E) the salt tends to neutralize the cholesterol in the egg
Q:
Two balls have the same shape and size but one is denser than the other. When they are dropped in air, which has the greater acceleration? Do not ignore air resistance.
A) The heavier ball
B) The lighter ball
C) They have the same acceleration
D) The heavier ball if atmospheric pressure is high, they lighter ball if it is low
E) The lighter ball if atmospheric pressure is high, the heavier ball if it is low
Q:
A cork floats in water in a bucket resting on the floor of an elevator. The elevator then accelerates upward. During the acceleration:
A) the cork is immersed more
B) the cork is immersed less
C) the cork is immersed the same amount
D) at first the cork is immersed less but as the elevator speeds up it is immersed more
E) at first the cork is immersed more but as the elevator speeds up it is immersed less
Q:
A blast of wind tips a sailboat in the clockwise direction when viewed from the stern. When the wind ceases the boat rotates back toward the upright position if, when it is tilted, the center of buoyancy:
A) is above the center of gravity
B) is below the center of gravity
C) is to the right of the center of gravity
D) is to the left of the center of gravity
E) coincides with the center of gravity