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Algebra-Based Physics is an introductory course designed for students seeking a foundational understanding of the core principles of physics without requiring calculus. The course covers key topics such as motion, forces, energy, waves, electricity, and magnetism, emphasizing conceptual understanding and problem-solving skills using algebraic methods. Through lectures, laboratory experiments, and practical applications, students develop a strong grasp of how physical laws govern the natural world and gain experience in applying these laws to real-life situations. This course is ideal for students pursuing careers in health sciences, biology, or fields that require a solid background in physics without the need for advanced mathematics.
Recommended Textbook Physics 4th Edition by James S. Walker
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Q1) Convert 1.2 × 10<sup>-3</sup> to decimal notation.
A) 1.200
B) 0.1200
C) 0.0120
D) 0.0012
E) 0.00012
Answer: D
Q2) The length of the Appalachian Trail is 2,015 miles. How long is it in kilometers?
A) 3,245 km
B) 1,251 km
C) 3,112 km
D) 1,008 km
E) 963 km
Answer: A
Q3) There are 640 acres in a square mile, and 5280 feet in one mile. How many acres are there in a hectare, a square one hundred meters on each side?
Answer: 2.47 acres
Q4) What are the dimensions of velocity?
Answer: [L]/[T]
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Q1) Suppose that an object is moving with constant acceleration. Which of the following is an accurate statement concerning its motion?
A) In equal times its speed changes by equal amounts.
B) In equal times its velocity changes by equal amounts.
C) In equal times it moves equal distances.
D) The object is not moving; it is at rest.
E) A statement cannot be made without additional information.
Answer: B
Q2) An object is thrown upwards with a speed of 14 .0 m/s. How long does it take it to reach its maximum height?
A) 1.22 s
B) 1.43 s
C) 3.14 s
D) 4.15 s
E) 5.31 s
Answer: B
Q3) Figure 2-2 represents the position of a particle as it travels along the x-axis. What is the average speed of the particle between t = 2 s and t = 4 s?
Answer: 1 m/s
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Q1) Vector quantities are represented in terms of their magnitude and direction.
A)True
B)False
Answer: True
Q2) You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat
A) due west.
B) due north.
C) due south.
D) in a southwesterly direction.
E) in a northwesterly direction.
Answer: E
Q3) Mass is a vector quantity.
A)True
B)False
Answer: False
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Q1) A rock is thrown from ground level at some angle above the horizontal with a certain velocity. It reaches its highest point and starts falling down. What is the magnitude of the velocity of the rock right before it hits the ground?
A) It is equal to its initial vertical velocity.
B) It is equal to its initial horizontal velocity.
C) It is equal to the magnitude of its initial velocity.
D) 0
E) Cannot be determined without additional information.
Q2) A bullet is fired from ground level with a speed of 150 m/s at an angle 30.0° above the horizontal at a location where g = 10.0 m/s<sup>2</sup>. What is the vertical component of its velocity when it is at the highest point of its trajectory?
A) 0 m/s
B) 10 m/s
C) 75.0 m/s
D) 130 m/s
E) 150 m/s
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Q1) A golf club hits a golf ball with a force of 2400 N. The golf ball hits the club with a force
A) slightly less than 2400 N.
B) exactly 2400 N.
C) slightly more than 2400 N.
D) close to 0 N.
E) Cannot be determined without additional information.
Q2) A 50.0-kg crate is being pulled along a horizontal, smooth surface. The pulling force is 10.0 N and is directed 20.0° above the horizontal. What is the acceleration of the crate?
A) 0.0684 m/s<sup>2</sup>
B) 0.188 m/s<sup>2</sup>
C) 0.200 m/s<sup>2</sup>
D) 0.376 m/s<sup>2</sup>
E) 0.0728 m/s<sup>2</sup>
Q3) The locking mechanism for the seatbelt of a car makes use of the fact that the apparent vertical direction (i.e. the direction in which a plumb bob hangs) changes with the car's deceleration. In a certain collision, the deceleration of a car is 5.00 g. What angle does the apparent vertical make with the true vertical?
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Q1) What type of acceleration does an object moving with constant speed in a circular path experience?
A) free fall.
B) terminal acceleration.
C) constant acceleration.
D) linear acceleration.
E) centripetal acceleration.
Q2) A 22.0-kg crate is pulled along a horizontal floor by the ideal arrangement shown in Figure 6-9. The force F is 300 N. The coefficient of friction between the crate and the floor is 0.270. What is the acceleration of the crate?
A) 4.17 m/s<sup>2</sup>
B) 6.57 m/s<sup>2</sup>
C) 2.34 m/s<sup>2</sup>
D) 4.85 m/s<sup>2</sup>
E) 9.65 m/s<sup>2</sup>
Q3) You are driving your car and set your sunglasses on the dashboard. When you make a left turn, the sunglasses go sliding off to the right. Explain.
Q4) Why does a cyclist tilt her bicycle on a curve?
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Q1) The ratio of kinetic energy of object A to the kinetic energy of object B is 2: 1. Object A is moving with a speed of 6.0 m/s and object B is moving with a speed of 2.0 m/s. If the mass of object A is 4.0 kg then what is the mass of object B?
A) 2.0 kg
B) 4.0 kg
C) 8.0 kg
D) 18 kg
E) 16 kg
Q2) The ratio of power outputs of Jack and Jill is 2: 1 to complete a certain amount of work. If Jill takes 4 minutes to complete this work, how long will Jack take to finish the same work?
A) 2 minutes
B) 1.4 minutes
C) 8 minutes
D) 6 minutes
E) 4 minutes
Q3) Work is a vector quantity.
A)True
B)False
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Q1) Kinetic energy may be positive or negative.
A)True
B)False
Q2) An 8 kg object moving with an initial velocity of 4 m/s comes to rest due to friction after it travels a horizontal distance of 10 m. If the initial speed of the object is doubled, what distance will it travel before coming to rest? Use g = 10 m/s<sup>2</sup>.
A) 10 m
B) 20 m
C) 30 m
D) 40 m
E) 80 m
Q3) Refer to Figure 8-7. What is the potential energy of the mass M<sub>1</sub> just before it touches the ground?
A) 2.3 J
B) 2.5 J
C) 0 J
D) 4 J
E) 5.2 J
Q4) State the Conservation of Mechanical Energy
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Q1) A 900-kg car traveling 30.0° south of east at 12.0 m/s collides with a 750-kg car traveling north at 17.0 m/s. The cars stick together. What is the speed of the wreckage just after the collision?
A) 7.21 m/s
B) 12.2 m/s
C) 20.4 m/s
D) 25.0 m/s
E) 17.3 m/s
Q2) The impulse delivered to an object is equal to the change in the object's velocity.
A)True B)False
Q3) A 0.140-kg baseball is dropped from rest from a height of 2.2 m above the ground. It rebounds to a height of 1.6 m. What change in the ball's momentum occurs when the ball hits the ground?
A) 0.117 kgm/s upwards
B) 0.117 kgm/s downwards
C) 1.70 kgm/s upwards
D) 0.350 kgm/s upwards
E) 0.350 kgm/s downwards
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Q1) A pencil, 15.7 cm long, is released from a vertical position with the eraser end resting on a table. The eraser does not slip. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table?
A) 17.2 rad/s
B) 7.23 rad/s
C) 3.70 rad/s
D) 24.5 rad/s
E) 16.8 rad/s
Q2) Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that
A) Jacques has a greater angular velocity than George.
B) Jacques and George have the same angular velocity.
C) Jacques has a smaller angular velocity than George.
D) both have zero angular velocities.
E) Cannot tell which one has the greater angular velocity without knowing their masses.
Q3) Mass can be considered concentrated at the center of mass for rotational motion.
A)True
B)False
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Q1) A 15.0-kg child is sitting on a playground teeter-totter, 1.50 m from the pivot. What force, applied 0.300 m on the other side of the pivot, is needed to make the child lift off the ground?
A) 75.0 N
B) 736 N
C) 22.5 N
D) 44.1 N
E) 66.2 N
Q2) A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of 0.100 kgm<sup>2</sup>, and the wheel slows to a stop in 160 s, what is the magnitude of the retarding torque?
A) 1.00 Nm
B) 0.00750 Nm
C) 0.0787Nm
D) 1.33 Nm
E) 1.67 Nm
Q3) State the conditions for static equilibrium.
Q4) When a car decelerates, its front end goes down. Explain.
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Q1) The ground rises and sinks regularly because of tidal effects.
A)True
B)False
Q2) An astronaut is piloting a spacecraft, which is in a circular orbit around Earth. A space station is ahead, on the same circular orbit. If he fires his rockets briefly to decrease the forward speed of the rocket, what will happen?
Q3) Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.0060 m/s<sup>2</sup> and the escape velocity is only 10.1 m/s. What is the mass of Eros? G = 6.67 x 10<sup>-11</sup> N·m<sup>2</sup>/kg<sup>2</sup>.
A) 2.3 × 10<sup>16</sup> kg
B) 3.5 × 10<sup>12</sup> kg
C) 6.5 × 10<sup>15</sup> kg
D) 4.9 × 10<sup>14</sup> kg
E) 6.7 × 10<sup>13</sup> kg
Q4) Why are planets and stars approximately spherical, whereas asteroids and meteorites are shaped like ordinary rocks?
Q5) State Kepler's Third Law of Orbital Motion
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Q1) An underdamped spring-mass system consists of a spring with a force constant of 2.00 N/m and a mass of 550 g. It is observed that the oscillations decrease in magnitude by 10.0% every 360 s. What is the value of the damping constant for the system?
A) 3.22 × 10<sup>-4</sup> Ns/m
B) 2.16 × 10<sup>-4</sup> Ns/m
C) 11.7 × 10<sup>-4</sup> Ns/m
D) 5.85 × 10<sup>-4</sup> Ns/m
E) 8.95 × 10<sup>-4</sup> Ns/m
Q2) A mass is oscillating on a spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time, if x is equal to 8.3 cm at t = 0 s.
Q3) In designing buildings to be erected in an area prone to earthquakes, should you try to have a small or a large amount of damping?
Q4) A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? (b) At what location are the kinetic energy and the potential energy the same?
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Q1) Which part of a vibrating string experiences the maximum acceleration?
A) nodes
B) ends
C) antinodes
Q2) The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m<sup>-1</sup>)x - (7.22 s<sup>-1</sup>)t]. What is the wavelength of the wave?
A) 3.25 m
B) 1.93 m
C) 0.870 m
D) 0.308 m
E) 0.139 m
Q3) The speed of surface waves in deep water is given by v = gT/2 . What is the wavelength of a wave that has a period of 3.00 s?
A) 4.68 m
B) 29.4 m
C) 14.1 m
D) 44.1 m
E) 39.4 m
Q4) What is the audible range of sound frequencies?
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Q1) Water flows in the vertical pipe shown in Figure 15-12. At A the diameter is 5.00 cm and at B the diameter is 4.00 cm. The fluid in the manometer is mercury, which has a density of 13,600 kg/m<sup>3</sup>. The manometer reading h is 4.50 cm. What volume of water is flowing through the pipe per second?
A) 0.0206 m<sup>3</sup>/s
B) 0.00545 m<sup>3</sup>/s
C) 0.372 m<sup>3</sup>/s
D) 0.186 m<sup>3</sup>/s
E) 0.718 m<sup>3</sup>/s
Q2) The pressure differential across a wing cross section due to the difference in air flow is explained by
A) Pascal's Principle.
B) Bernoulli's equation.
C) Poiseuille's law.
D) Archimedes Principle.
E) Torricelli's law.
Q3) State Archimedes' Principle.
Q4) State Pascal's Principle
Q5) What is meant by gauge pressure?
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Q1) How much power does a sphere with a radius of 10 cm radiate if is has an emissivity e = 1.0 and is kept at a temperature of 400 K? The Stefan-Boltzmann constant is 5.67 x 10<sup>-8</sup> W/(m<sup>2</sup>·K<sup>4</sup>).
A) 60 W
B) 70 W
C) 180 W
D) 210 W
E) 360 W
Q2) The type of heat transfer that occurs between warm food and the air in the room is principally
A) convective.
B) conductive.
C) radiative.
D) countercurrent.
E) evaporation.
Q3) Does it make sense to say that an object has twice as much heat as another? Why?
Q4) Radiative heat transfer requires a fluid to mediate the energy transfer.
A)True
B)False

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Q1) A 50-kg air conditioner is placed on top of a concrete pad with a cross-sectional area of 3.0 m<sup>2</sup> and 20 cm thick. What is the change in thickness of the pad? Young's modulus for concrete is 2.3 × 10<sup>10</sup> N/m<sup>2</sup>.
A) 1.4 × 10<sup>-9</sup> m
B) 2.8 × 10<sup>-9</sup> m
C) 1.4 × 10<sup>-8</sup> m
D) 1.4 × 10<sup>-7</sup> m
E) 2.8 × 10<sup>-8</sup> m
Q2) A 25-kg television set rests on four rubber pads, each having a height of 1.0 cm and a radius of 0.60 cm. A 200-N horizontal force is applied to the television set. How far does it move sideways? The shear modulus of rubber is 2.6 × 10<sup>6</sup> N/m<sup>2</sup>.
A) 6.8 mm
B) 3.4 mm
C) 1.7 mm
D) 1.5 mm
E) 1.3 mm
Q3) State Charles's law.
Q4) State Boyle's law.
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Q1) A heat engine operating at maximum efficiency has an efficiency of 25%. The temperature of the cold reservoir is 300 K. What is the temperature of the hot reservoir?
A) 350 K
B) 375 K
C) 400 K
D) 450 K
E) 500 K
Q2) An ideal monatomic gas undergoes a reversible expansion to 1.5 times its original volume. In which of these processes does the gas have the largest loss of internal energy?
A) at constant pressure
B) if the pressure increases in proportion to the volume
C) if the pressure decreases in proportion to the volume
D) at constant temperature
E) adiabatically
Q3) The entropy of a system remains constant during an adiabatic change even if the change is irreversible.
A)True
B)False
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Q1) A charged rod carrying a negative charge is brought near two spheres that are in contact with each other but insulated from the ground. If the two spheres are then separated, what kind of charge will be on the spheres?
A) The sphere near the charged rod becomes positive and the other becomes negative.
B) The sphere near the charged rod becomes negative and the other becomes positive.
C) The spheres do not get any charge.
D) None of the other choices is correct.
Q2) An atomic nucleus has a charge of +40e. An electron is 10<sup>-9 </sup>m from the nucleus. What is the force on the electron?
A) 2.9 nN
B) 1000 C
C) 3.7 nN
D) 6.8 nN
E) 9.2 nN
Q3) A 5.0- C charge is placed at the 0 cm mark of a meter stick and a -4.0 C charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field zero?
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Q1) A surface on which all points are at the same potential is referred to as
A) a constant electric force surface.
B) a constant electric field surface.
C) an equipotential surface.
D) an equivoltage surface.
E) a dielectric surface.
Q2) Two equal point charges of magnitude 4.0 C are situated along the x-axis at x<sub>1</sub> = -2.0 m and x<sub>2</sub> = -2.0 m. What is the electric potential energy of this system of charges?
A) -36 mJ
B) 36 mJ
C) 0 J
D) -72 mJ
E) 72 mJ
Q3) If you were a parallel plate capacitor manufacturer, state three ways you might make larger valued capacitors.
Q4) The capacitance of a parallel plate capacitor is directly proportional to its plate separation.
A)True
B)False

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Q1) Three capacitors are connected as shown in Figure 21-17. What is the equivalent capacitance between points A and B?
A) 1.7 F
B) 4.0 C
C) 7.1 F
D) 12 F
E) 8.0 F
Q2) A light bulb operating at a voltage of 120 Volt has a power of 60 W. What is the current flowing through this bulb?
A) 1.5 A
B) 2.5 A
C) 0.5 A
D) 2 A
E) 1 A
Q3) Which one of the following is the correct expression for electric current?
A) I = C/ t
B) I = R/ t
C) I = V/ t
D) I = Q/ t
E) None of the other answers is correct.
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Q1) An electron moving perpendicular to a magnetic field of 3.2 × 10<sup>-2</sup> T moves in a circle of radius 0.40 cm. How fast is this electron moving?
A) 2.3 × 10<sup>7</sup> m/s
B) 1.9 × 10<sup>-53</sup> m/s
C) 1.9 × 10<sup>-30</sup> m/s
D) 3.0 × 10<sup>9</sup> m/s
E) 0.80 × 10<sup>7</sup> m/s
Q2) A rectangular coil, with corners labeled ABCD, of length L and width w is placed in a magnetic field B as shown in Figure 22-3. If there is a current I flowing through this coil, what is the force acting on section AB of this coil?
A) ILB sin
B) ILB cos
C) ILB
D) 0 N
E) ILB/2
Q3) Ten meters away from a long straight wire, the field is 10<sup>-4</sup> Tesla. What current flows through the wire?
Q4) Describe ferromagnetism.
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Q1) A bar magnet is placed with its north pole pointing toward a coil of wire that has a cross-sectional area of 0.02 m<sup>2</sup> and 6 turns, as shown in Figure 23-7(a). What is the magnitude of the induced emf in the coil of wire?
A) 0.04 V
B) 0.03 V
C) 0.01 V
D) 0.02 V
E) 0 V
Q2) A conducting rod with a length of 25 cm is placed on a U-shaped metal wire that has a resistance R of 8.0 as shown in Figure 23-9. The wire and the rod are placed in the plane of the paper. A constant magnetic field of strength 0.40 T is applied perpendicular into the paper. An applied force moves the rod to the right with a constant speed of 6.0 m/s. What is the magnitude and direction of the induced current in the wire?
A) 17 mA clockwise
B) 17 mA counterclockwise
C) 75 mA counterclockwise
D) 75 mA clockwise
E) 52 mA clockwise
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Q1) A 120-V rms voltage at 1000 Hz is applied to a 2.00-mH inductor, a 4.00- F capacitor and a resistor. If the rms value of the current in this circuit is 0.400 A, what is the value of the resistor?
A) 299
B) 95.1
C) 423
D) 120
E) 240
Q2) In a RLC circuit, a second capacitor is connected in series with the capacitor previously in the circuit. What is the effect of this change on the impedance of the circuit?
A) It increases.
B) It decreases.
C) It does not change.
D) It increases for frequencies below resonance and decreases for frequencies above resonance.
E) It decreases for frequencies below resonance and increases for frequencies above resonance.
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Q1) For an xyz-coordinate system shown in Figure 25-2, if the E-vector is in the +z direction, and the B-vector is in the +x direction, what is the direction of propagation of the electromagnetic waves?
A) +x
B) -x
C) +y
D) -y
E) +z
Q2) A car is approaching a radio station at a speed of 25.0 m/s. If the radio station broadcasts at a frequency of 74.5 MHz, what change in frequency does the driver observe?
A) 98.3 Hz
B) 6.21 Hz
C) 726 Hz
D) 67.0 Hz
E) 64.5 Hz
Q3) Electromagnetic waves do not require a medium to be transmitted.
A)True
B)False
Q4) A cordless phone operates at 900 MHz. What is the associated wavelength?
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Q1) The reflection of light from a rough surface is called specular reflection.
A)True
B)False
Q2) An object 2.0 cm in height is placed at the center of curvature C in front of a concave mirror. What is the height of its image?
A) -0.50 cm
B) -1.0 cm
C) -1.5 cm
D) -2.0 cm
E) -6 cm
Q3) A concave mirror is also known as a diverging mirror.
A)True
B)False
Q4) The index of refraction for a given material is directly proportional to the frequency of light.
A)True
B)False
Q5) An object is placed 9.5 cm from a lens of focal length 24 cm.
(a) Where is the image formed?
(b) What is the magnification?

28
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Q1) The focal length of the objective of a telescope is 0.2 m and the eyepiece has a focal length of 1.6 m. What is the length of this telescope?
A) 8.0 m
B) 1.4 m
C) 0.90 m
D) 1.6 m
E) 1.8 m
Q2) The world's largest refracting telescope is operated at the Yerkes Observatory in Wisconsin. It has an objective of diameter of 1.02 m. Suppose such an instrument could be mounted on a spy satellite at an elevation of 300. km above the surface of the Earth. What is the minimum separation of two objects on the ground if their images are to be clearly resolved by this lens?
(Assume an average wavelength of 0.55 m for white light.)
Q3) Consider a magnifying glass with a power of 3.0 D.
(a) What is the maximum magnification for a person with a near point of 25. cm?
(b) What is the magnification when viewing with a relaxed eye?
Q4) A student wishes to build a telescope. She has available an eyepiece of focal length -5.0 cm. What focal length objective is needed to obtain a magnification of 10x?
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Q1) Light of wavelength 500 nm illuminates a soap film ( n = 1.33). What is the minimum thickness of film that will give an interference when the light is incident normally on it?
A) 24 nm
B) 56 nm
C) 94 nm
D) 188 nm
E) 376 nm
Q2) The wavelength of light in a thin film is 360 nm and the wavelength of light in vacuum is 469 nm. What is the index of refraction for the film?
A) 1.10
B) 1.30
C) 1.50
D) 1.70
E) 1.90
Q3) The law of reflection, as well as the law of refraction, can be derived using Huygens' principle.
A)True
B)False
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Q1) In order to see a distant star during a total eclipse of the Sun you must look for it in a direction that is farther from the Sun than the direction you would normally look for the star.
A)True
B)False
Q2) A spaceship traveling at constant speed passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?
A) the Earth frame of reference
B) the Mars frame of reference
C) the spaceship frame of reference
D) any inertial frame of reference
E) any frame of reference, inertial or not
Q3) At what speed is the mass of an electron double its rest mass?
A) 0.500c
B) 0.650c
C) 0.707c
D) 0.866c
E) 0.960c
Q4) How fast must something be traveling if its mass increases by 10%?
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Q1) A photon has an energy of 6.60 eV. To what wavelength does this energy correspond?
A) 100 nm
B) 118 nm
C) 151 nm
D) 173 nm
E) 189 nm
Q2) The cosmic background radiation permeating the universe has the spectrum of a 2.7 K thermal radiator. What is the peak wavelength?
Q3) A certain photon after being scattered from a free electron at rest moves at an angle of 120° with respect to the incident direction. If the wavelength of the incident photon is 0.611 nm, what is the kinetic energy of the recoiling electron?
A) 1.5 × 10<sup>-18</sup> J
B) 2.1 × 10<sup>-18</sup> J
C) 3.1 × 10<sup>-18</sup> J
D) 4.3 × 10<sup>-18</sup> J
E) 5.2 × 10<sup>-18</sup> J
Q4) What is the energy, in eV, of a photon of wavelength 550. nm?
Q5) Our bodies, at 37.°C, emit radiation which peaks at what wavelength?
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Q1) What is the wavelength of the emitted photon if an electron in the hydrogen atom makes a transition from n = 2 state to the ground state?
A) 121.5 nm
B) 203.1 nm
C) 243.0 nm
D) 388.8 nm
E) 411.1 nm
Q2) To which of the following values of n does the shortest wavelength in the Balmer series correspond?
A) 3
B) 5
C) 7
D) 1
E) (very large)
Q3) The energy for n = 4 and = 0 state is greater than the energy for n = 3 and = 2 state.
A)True
B)False
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Q1) Gravity waves are produced when a mass accelerates.
A)True
B)False
Q2) What is the approximate nuclear radius of an isotope of sodium with 11 protons and 12 neutrons?
Q3) When an unstable nucleus decays by emitting an alpha particle, the atomic mass number of the nucleus
A) increases by 4.
B) increases by 2.
C) decreases by 2.
D) decreases by 4.
E) remains unchanged.
Q4) The radius of a nucleus is proportional to what power of the mass number?
A) 1/2
B) 1/3
C) 1/4
D) 2/5
E) 3/8
Q5) What combination of quarks produces a proton and what are the electric charges on these quarks, expressed in terms of e?
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