Oscillatory Motion
Fluids
Thermodynamics and the Kinetic Theory of Gases
Quantum Theory and
The Atom
Mystery Questions
100
What is the length of a pendulum whose period, at the Equator, is 1 s?
(A) 0.15 m
(B) 0.25 m
(C) 0.30 m
(D) 0.45 m
(E) 1.0 m
(B) 0.25 m
If we use the formula for the period of a pendulum, T = 2π√(l/g), and square both sides, we can solve for the length:
l = T2 * g/(4π2)
Using the values given in the question, we find that l = 0.25 m.
100
The rate of flow of a liquid from a hole in a container depends on all of the following except:
(A) the density of the liquid.
(B) the height of the liquid above the hole.
(C) the area of the hole.
(D) the acceleration of gravity.
(E) the diameter of the hole.
(A) the density of the liquid.
The flow rate of a liquid from a hole does not depend on the density of the liquid.
100
As the temperature of an ideal gas increases, the average kinetic energy of its molecules ...?
The absolute temperature of an ideal gas is directly proportional to the average kinetic energy of its molecules. Hence, the average kinetic energy increases with temperature.
100
How many photons are associated with a beam of light having a frequency of 2 × 1016 Hz and a detectable energy of 6.62 × 10-15 J?
(A) 25
(B) 500
(C) 135
(D) 8
(E) 80
(B) 500
If E equals the total detectable energy and Ep equals the energy of a photon, then
N = E/Ep = E/(hf)
= (6.63 × 10-15 J) / (1.326 × 10-17 J) = 500
100
Gravitation:
What is the gravitational force of attraction between two trucks, each of mass 20 000 kg, separated by a distance of 2m?
We use the formula for gravitational force:
F = GM1M2/R2
Substituting the given values (don't forget to square the distance!) yields F = 0.0067 N.
200
When a 0.05-kg mass is attached to a vertical spring, it is observed that the spring stretches 0.03 m. The system is then placed horizontally on a frictionless surface and set into simple harmonic motion. What is the period of the oscillations?
(A) 0.75 s
(B) 0.12 s
(C) 0.35 s
(D) 1.3 s
(E) 2.3 s
(C) 0.35 s
We first find the spring constant. From F = kx, we see that;
F = mg = (0.05)(9.8) = 0.49N
Thus
k = F/x = 0.49/0.03 = 16.3 N/m
Now the period is given by the formula T = 2π√(m/k). Using the values given in the equation, we find that T = 0.35 s.
200
Bernoulli's equation is based on which law of physics?
(A) conservation of linear momentum.
(B) conservation of angular momentum.
(C) Newton's first law of motion.
(D) Newton's law of gravity.
(E) conservation of energy.
(E) conservation of energy.
Bernoulli's principle was developed as an application of conservation of energy.
200
At constant temperature, an ideal gas is at a pressure of 30 cm of mercury and a volume of 5 L. If the pressure is increased to 65 cm of mercury, the new volume will be ...?
At a constant temperature, an ideal gas obeys Boyle's law. Since we are making a two-position comparison, we can use the given units for pressure and volume. Substituting the given values into Boyle's law, we obtain (30)(5) = (65)(V2), which implies that V2 = 2.3 L.
200
How much energy is needed to ionize a hydrogen atom in the n = 4 state?
(A) 0.84 eV
(B) 13.6 eV
(C) 12.75 eV
(D) 10.2 eV
(E) 3.4 eV
(A) 0.84 eV
In the n = 4 state, the energy level is -0.85 eV. Thus, to ionize the electron in this state, +0.85 eV must be supplied.
200
At 25°C, a sound wave takes 3 s to reach a receiver. how far away is the receiver from the source?
At 25°C, the speed of sound is 331 + (0.6)(25) = 346 m/s. Since x = vt,
x = (346)(3) = 1038 m
300
Which of the following is an expression for the maximum velocity of an oscillating mass-spring system?
(A) √[(Ak)/m]
(B) √(A2mk)
(C) √[(A2m)/k]
(D) √[(A2k)/m]
(E) Akm
(D) √[(A2k)/m]
Since vmax = Aω and ω = √(k/m), bringing A back under the radical sign makes the equation equal to √[(A2k)/m]
300
A moving fluid has an average pressure of 600 Pa as it exits a circular hole with a radius of 2 cm at a velocity of 60 m/s. what is the approximate power generated by the fluid?
The power is equal to the product of pressure and the flow rate. The flow rate is equal to the product of the velocity and the cross-sectional area (which is a circle of radius 0.02 m). The area is given by πr2 = 1.256 × 10-3 m2. When we multiply this area by the velocity and the pressure, we get 45.2 W as a measure of the generated power.
300
How many molecules of Helium are required to fill a balloon with a diameter of 50 cm at a temperature of 27°C?
From the ideal gas formula, we know that PV = NkT, where N equal the number of molecules and k is Boltzmann's constant. For a 50-cm-diameter balloon, the radius will be 0.25 m. One atmosphere is equal to 101,000 Pa of pressure. The volume of a sphere is given by V = (4/3)πR3, which equals 0.065 m3 upon substitution.
We know also that N = PV/kT, where T is equal to 300 K in this problem. Substituting all known values gives
N = (101,000 × 0.065)/[(1.38 × 10-23)(300)]
= 1.59 × 1024 molecules
300
What is the momentum of a photon associated with yello light that has a wavelength of 5500 Å (one angstrom is 100 picometres)?
The wavelength must first be converted into metres, then we use p = h/λ:
p = (6.63 × 10-34)/[(5500)(1 × 10-10)]
= 1.2 × 10-27 kg m/s
300
Gravitation:
A "black hole" theoretically has an escape velocity that is greater than or equal to the velocity of light (3 × 108 m/s). If the effective mass of the black hole is equal to the mass of the Sun (2 × 1030 kg), what is the effective "radius" (called "Schwarzchild radius") of the black hole?
We know that escape velocity is given by vesc = √[2GM/R]. To find R, we need to square both sides, and then solve for radius. This yields R = 2GM/v2. Substituting the given values yields R = 3000. (This is only a "theoretical" size for the black hole. For bonus points, try calculating the value of g on such an object!)
400
A mass of 0.3 kg is connected to a massless spring with a force constant of 20 N/m. The system oscillates horizontally on a frictionless surface with an amplitude of 4 cm. What is the velocity of the mass when it is 2 cm from its equilibrium position?
The formula for any intermediary velocity is v = √[(k/m)(A2 - x2)]. Before substituting the known values, we must change centimeters to meters: 4 cm = 0.04 m and 2 cm = 0.02 m. Then, using these values form amplitude and position, we find that v = 0.28 m/s.
400
Alcohol has a specific gravity of 0.79. If a barometer consisting of an open-ended tube placed in a dish of alcohol is used at sea level, to what height in the tube will the alcohol rise?
The pressure exerted by the air is balanced by the column of liquid alcohol in equilibrium:
h = P/(ρg) = (1.01 × 105 N/m2)/(790 kg/m3 × 9.8 m/s2) = 13.1 m
400
The first law of thermodynamics is a restatement of which law?
The first law of thermodynamics expresses the conservation of energy.
400
A radioactive atom emits a gamma ray photon. As a result
(A) the energy of the nucleus is decreased
(B) the charge in the nucleus is decreased
(C) the ground-state energy is decreased
(D) the force on an orbiting electron is decreased
(E) None of the preceding statements are correct.
(A) the energy of the nucleus is decreased
Since photons do not have any rest mass, their emission releases nuclear energy only.
400
A jet engine's noise is coming into a window 1.0 m wide by 1.2 m high. If the sound level is 140 dB, at what rate does energy enter the window?
The formula for sound level in decibels is
β = 10 log (I/I0)
where I0, a barely audible intensity, equals 10-12 W/m2. In our problem, β = 140 dB, and we must solve for intensity I. If we divide by 10, substitute for I0, and then exponentiate by raising each side as a power of 10, we get, after cross-multiplying, I = 100 W/m2.
The rate of energy per second is the power emitted, in watts. we must multiply 100 W/m2 by the area of our window, which is 1.2m2. Thus, the rate at which energy is emitted is 120 W.
500
A 2-kg mass is oscillating horizontally on a frictionless surface when attached to a spring. The total energy of the system is observed to be 10 J. If the mass is replaced by a 4-kg mass, but the amplitude of the oscillations and the spring remain the same, the total energy of the system will be ...?
The maximum energy in the mass-spring system can be expressed independently of the mass; it depends on the force constant and the square of the amplitude. Thus, if the spring and amplitude of oscillations remain the same, so will the total energy of the system (10 J).
500
A 2-N force is used to push a small piston 10 cm downward in a simple hydraulic machine. if the opposite large piston rises by 0.5 cm, what is the maximum weight the large piston can lift?
We need to use the conservation of work-energy in this problem. The work done on the small piston must equal the work done by the large piston. Since the ratio of displacements is 20:1, the large piston will be able to support a maximum load of 40 N (since 2 N × 20 = 40 N).
500
Which of the following graphs represents the relationship between pressure and volume for an ideal confined gas at constant temperature? (V is on x-axis, P is on y-axis)
(A) Linear graph
(B) Exponential graph
(C) Logarithmic graph
(D) Constant graph
(E) Rectangular hyperbola with horizontal/vertical asymptotes (e.g f(x) = 1/x)
(E) Rectangular hyperbola with horizontal/vertical asymptotes
Boyle's law relates the pressure and volume in an ideal gas. This is an inverse relationship that looks like a hyperbola.
500
Explain why increasing the intensity of electromagnetic radiation on a photoemissive surface does not affect the kinetic energy of the ejected photoelectrons. Why is this kinetic energy referred to as the "maximum kinetic energy"?
In the quantum theory of light, each photon interacts with one, and only one, electron. Thus, if the energy of a photon is based on its frequency, the intensity of light is just the number of photons. Thus, each electron emerges with the same kinetic energy. This is true for 1 or 1 billion electrons. Therefore, we refer to this kinetic energy as the "maximum kinetic energy."
500
Electrostatics:
Four identical point charges (Q = +3 μC) are arranged in the form of a rectangle (landscape orientation) with length = 7 cm and width = 5 cm.
What are the magnitude and the direction of the net electric force on the charge in the lower left corner due to the other three charges?
Since all the charges are positive, the lower-left-corner charge will experience mutual repulsions from the other three.
The magnitude of each force is given by Coulomb's law. The diagonal distance was determined by using the Pythagorean theorem. The three force magnitudes are therefore calculated to be:
F1 = (9 × 109)(3 × 10-6)(3 × 10-6)/(0.07)2 = 16.53 N
F2 = (9 × 109)(3 × 10-6)(3 × 10-6)/(0.086)2 = 10.95 N
F3 = (9 × 109)(3 × 10-6)(3 × 10-6)/(0.05)2 = 32.4 N

Now, F1 acts to the left and F3 acts downward, so no further vector reductions are necessary. However, F2 acts at some angle toward the lower left, given by Θ. To find the angle, we recall that tan Θ = 5/7, which implies that Θ = 35.53°. Both components of F2 will be negative by convention.
We can now write
F2x = ±10.98 cos 35.53 = ±8.91 N
and
F2y = ±10.95 sin 35.53 = ±6.36 N
The resultant or net force acting on the lower-left-corner charge is the vector sum of these charges. we can find the components of this force by simply adding up the forces in the same directions:
Fx = -16.83 - 8.91 = -25.44 N
Fy = -32.40 - 6.36 = -38.76 N
The magnitude of the net force F is given by the Pythagorean theorem and is equal to 46.3 N. The direction of this force is given by
tan ϕ = Fx/Fy = 38.76/25.44 = 1.5
This implies that ϕ = 56.7° relative to the negative x-axis.
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