Spring Not-Break Review Assignment

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1 Name AP Physics B Spring Not-Break Review Assignment Date Mrs. Kelly. A kilogram block is released from rest at the top of a curved incline in the shape of a quarter of a circle of radius R. The block then slides onto a horizontal plane where it finally comes to rest 8 meters from the beginning of the plane. The curved incline is frictionless, but there is an 8 newton force of friction on the block while it slides horizontally. Assume g = 0 m/s. a. Determine the magnitude of the acceleration of the block while it slides along the horizontal plane. b. What time elapses while the block is sliding horizontally? c. Calculate the radius of the incline in meters.. A cylinder contains moles of an ideal monatomic gas that is initially at state A with a volume of.0 x 0 - m and a pressure of 4.0 x 0 5 Pa. The gas is brought isobarically to state B, where the volume is.0 x 0 - m. The gas is then brought at constant volume to state C, where its temperature is the same as at state A. The gas is then brought isothermally back to state A. a. Determine the pressure of the gas at state C. b. On the axes below, state B is represented by the point B. Sketch a graph of the complete cycle. Label points A and C to represent states A and C, respectively. c. State whether the net work done by the gas during the complete cycle is positive, negative, or zero. Justify your answer. d. State whether this device is a refrigerator or a heat engine. Justify your answer. 3. A charge Q = - 6 x 0-6 coulomb is fixed on the x-axis at +4.0 meters, and a charge Q = + 9 x 0-6 coulomb is fixed on the y-axis at meters, as shown on the diagram. a. Calculate the magnitude of the electric field E at the origin O due to charge Q. b. Calculate the magnitude of the electric field E at the origin O due to charge Q. c. On the axes, below left, draw and label vectors to show the electric fields E and E due to each charge, and also indicate the resultant electric field E at the origin. d. Calculate the electric potential V at the origin. A charge Q 3 = -4 x 0-6 coulomb is brought from a very distant point by an external force and placed at the origin. e. On the axes, below right, indicate the direction of the force on Q 3 at the origin. f. Calculate the work that had to be done by the external force to bring Q 3 to the origin from the distant point.

2 4. Two parallel conducting plates, each of area 0.30 m, are separated by a distance of.0 x 0 - m of air. One plate has charge +Q; the other has charge Q. An electric field of 5,000 N/C is directed to the left in the space between the plates, as shown in the diagram below. a. Indicate on the diagram which plate is positive (+) and which is negative (-). b. Determine the potential difference between the plates. c. Determine the capacitance of this arrangement of plates. An electron is initially located at a point midway between the plates. d. Determine the magnitude of the electrostatic force on the electron at this location and state its direction. e. If the electron is released from rest at this location midway between the plates, determine its speed just before striking one of the pates. Assume that gravitational effects are negligible. 5. A student is provided with a.0-v battery of negligible internal resistance and four resistors with the following resistances: 00 Ω, 30 Ω, 0 Ω, and 0 Ω. The student also has plenty of wire of negligible resistance available to make connections as desired. a. Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but in which the current from the battery is as small as possible. b. Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but in which the current from the battery is as large as possible (without short circuiting the battery). The battery and resistors are now connected in the circuit shown. c. Determine the following for this circuit. i. The current in the 0-Ω resistor ii. The total power consumption of the circuit d. Assuming that the current remains constant, how long will it take to provide a total of 0 kj of electrical energy to the circuit? 6. A proton of mass m p and change e is in a box that contains an electric field E, and the box is located in Earth s magnetic field B Earth. The proton moves with an initial velocity v vertically upward from the surface of Earth. Assume gravity is negligible. a. On the diagram above, indicate the direction of the electric field inside the box so that there is no change in the trajectory of the proton while it moves upward in the box. Explain your reasoning. b. Determine the speed of the proton while in the box if it continues to move vertically upward. Express your answer in terms of the fields and the given quantities. The proton now exits the box through the opening at the top. c. On the figure above, sketch the path of the proton after it leaves the box. d. Determine the magnitude of the acceleration a of the proton just after it leaves the box, in terms of given quantities and fundamental constants.

3 7. A square loop of wire of side 0.0 m has a total resistance of 0.60 Ω. The loop is positioned in a uniform magnetic field B of T. The field is directed into the page, perpendicular to the plane of the loop, as shown in the diagram below. a. Calculate the magnetic flux φ through the loop. The field strength now increases uniformly to 0.0 T in 0.50 seconds. b. Calculate the emf ε induced in the loop during this period. c. i) Calculate the magnitude I of the current in the loop during this period. ii) What is the direction of the current in the loop? clockwise counterclockwise Justify your answer. d. Describe a method by which you could induce a current in the loop if the magnetic field remained constant. 8. A hollow tube of length l open at both ends as shown above, is held in midair. A tuning fork with a frequency f o vibrates at one end of the tube and causes the air in the tube to vibrate at its fundamental frequency. Express your answers in terms of l (length) and f o. a. Determine the wavelength of the sound. b. Determine the speed of sound in the air inside the tube. c. Determine the next higher frequency at which this air column would resonate. The tube is submerged in a large, graduated cylinder filled with water. The tube is slowly raised out of the water and the same tuning fork, vibrating with frequency f O, is held a fixed distance from the top of the tube. d. Determine the height h of the tube above the water when the air column resonates for the first time. Express your answer in terms of l (length).

4 9. Blocks and of masses m and m, respectively, are connected by a light string, as shown below. These blocks are further connected to a block of mass M by another light string that passes over a pulley of negligible mass and friction. Blocks and move with a constant velocity v down the inclined plane which makes an angle θ with the horizontal. The kinetic frictional force on block is f and that on block is f. a) Draw and label all of the forces on block m. Express your answers to each of the following in terms of m, m, g, θ and f. b) Determine the coefficient of kinetic friction between the inclined plane and block. c) Determine the value of the suspended mass M that allows blocks and to move with constant velocity down the plane. d) The string between blocks and is now cut. Determine the acceleration of block while it is on the inclined plane. 0. Two identical objects, A and B, of mass M move on a one-dimensional, horizontal air track. Object B initially moves to the right with speed v o. Object A initially moves to the right with speed 3v 0, so that it collides with object B. Friction is negligible. Express your answers to the following in terms of M and v o. (a) Determine the total momentum of the system of the two objects. (b) A student predicts that the collision will be totally inelastic (the objects stick together on collision). Assuming this is true, determine the following for the two objects immediately after the collision. i. the speed ii. the direction of motion (left or right) When the experiment is performed, the student is surprised to observe that the objects separate after the collision and that object B subsequently moves to the right with a speed.5v o. (c) Determine the following for object A immediately after the collision. i. the speed ii. the direction of motion (left or right) (d) determine the kinetic energy dissipated in the actual experiment.. While exploring a sunken ocean liner, the principal researcher found the absolute pressure on the robot observation submarine at the level of the ship to be about 43 atmospheres. The density of seawater is 05 kg/m 3. (a) Calculate the gauge pressure p g on the sunken ocean liner. (b) Calculate the depth D of the sunken ocean liner. (c) Calculate the magnitude F of the force due to the water on a viewing port of the submarine at this depth if the viewing port has a surface area of m. Suppose that the ocean liner cam to rest at the surface of the ocean before it started to sink. Due to the resistance of the seawater, the sinking ocean liner then reached a terminal velocity of 0.0 m/s after falling for 30.0 seconds. (d) Determine the magnitude a of the average acceleration of the ocean liner during this period of time. (e) Assuming the acceleration was constant, calculate the distance d below the surface at which the ocean liner reached this terminal velocity. (f) Calculate the time t it took the ocean liner to sink from the surface to the bottom of the ocean.

5 . A pump, submerged at the bottom of a well that is 35 m deep, us used to pump water uphill to a house that is 50 m above the top of the well, as shown below, The density of water is,000 kg/m 3. All pressures are gauge pressures. Neglect the effects of friction, turbulence, and viscosity. (a) Residents of the house use 0.35 m 3 of water per day. The day s pumping is completed in hours during the day. i. Calculate the minimum work required to pump the water used per day. ii. Calculate the minimum power rating of the pump. (b) The average pressure the pump actually produces is 9.0 x 0 5 N/m. Within the well the water flows at 0.50 m/s and the pipe has a diameter of 3.0 cm. At the house the pipe diameter is.5 cm. i. Calculate the flow velocity when a faucet in the house is open. ii. Explain how you would calculate the minimum pressure at the faucet. 3. In a linear accelerator, protons are accelerated from rest through a potential difference to a speed of approximately 3. x 0 6 m/s. The resulting proton beam produces a current of x 0-6 A. (a) Determine the potential difference through which the protons were accelerated. (b) If the beam is stopped in a target, determine the amount of thermal energy that is produced in the target in one minute. The proton beam enters a region of uniform magnetic field B, as shown below, that causes the beam to follow a semicircular path. (c) Determine the magnitude of the field that is required to cause an arc of radius 0.0 meter. (d) What is the direction of the magnetic field relative to the axes shown above on the right? 4. Light of frequency 6.0 x 0 4 Hz strikes a glass/air boundary at an angle of incidence θ. The ray is partially reflected and partially refracted at the boundary, as shown. The index of refraction of this glass is.6 for light of this frequency. a. Determine the value of θ 3 if θ = 30. b. Determine the value of θ if θ = 30. c. Determine the speed of this light in the glass. d. Determine the wavelength of this light in the glass. e. What is the largest value of θ that will result in a refracted ray?

6 5. In an experiment, a beam of red light of wavelength 675 nm in air passes from glass into air as shown below left. The incident and refracted angles are θ and θ, respectively. In the experiment, angle θ is measured for various angles of incidence θ, and the sines of the angles are used to obtain the line shown in the following graph, below right. a) Assuming an index of refraction of.00 for air, use the graph to determine a value for the index of refraction of the glass for the red light. Explain how you obtained this value. b) For this red light, determine the following: i. The frequency in air ii. The speed in glass iii. The wavelength in glass c) The index of refraction of this glass is.66 for violet light, which has wavelength 45 nm in air. i. Given the same incident angle θ, show on the ray diagram above how the refracted ray for the violet light would vary from the refracted ray already drawn for the red light. ii. Sketch the graph of sin θ versus θ for the violet light on the figure above that shows the same graph already drawn for the red light. d) Determine the critical angle of incidence θ c for the violet light in the glass in order for total internal reflection to occur. 6. Light of wavelength 5.0 x 0-7 meter in air is incident normally (perpendicularly) on a double slit. The distance between the slits is 4.0 x 0-4 meter, and the width of each slit is negligible. Bright and dark fringes are observed on a screen.0 meters away from the slits. a. Calculate the distance between two adjacent bright fringes on the screen. The entire double-slit apparatus, including the slits and the screen, is submerged in water, which has an index of refraction.3. b. Determine each of the following for this light in water. i. The wavelength. ii. The frequency. c. State whether the distance between the fringes on the screen increases, decreases, or remains the same. Justify your answer. 7. Two small speakers S are positioned a distance of 0.75 m from each other, as shown in the diagram below. The two speakers are each emitting a constant 500 Hz tome, and the sound waves from the speakers are in phase with each other. A student is standing at point P, which is a distance of 5.0 m from the midpoint between the speakers, and hears a maximum as expected. Assume that reflections from nearby objects are negligible. Use 343 m/s for the speed of sound. (a) Calculate the wavelength of these sound waves. (b) The student moves a distance Y to point Q and notices that the sound intensity has decreases to a minimum. Calculate the shortest distance the student could have moved to hear this minimum. (c) Identify another location on the line that passes through P and Q where the student could stand in order to observe a minimum. Justify your answer. (d) i. ii. How would your answer to (b) change if the two speakers were moved closer together? Justify your answer. How would your answer to (b) change if the frequency emitted by the two speakers was increased? Justify your answer.

7 8. A sodium photoelectric surface with work function.3 ev is illuminated by electromagnetic radiation and emits electrons. the electrons travel toward a negatively charged cathode and complete the circuit shown below. The potential difference supplied by the power supply is increased, and when it reaches 4.5 V, no electrons reach the cathode. (a) For the electrons emitted from the sodium surface, calculate the following: i. The maximum kinetic energy ii. The speed at this maximum kinetic energy (b) Calculate the wavelength of the radiation that is incident on the sodium surface. (c) Calculate the minimum frequency of light that will cause photoemission from this sodium surface. 9. Consider the following nuclear fusion reaction that uses deuterium as fuel. 4 3 ( H ) He+ H + 0 (a) Determine the mass defect of a single reaction given the following information. n 4 H =. 04u He = u H =. 0078u 0 n =. 0087u (b) Determine the energy in Joules released during a single fusion reaction. (c) The United States requires about 0 0 J per year to meet its energy needs. How many deuterium atoms would be necessary to provide this magnitude of energy? (d) Assume the 0.05% of the hydrogen atoms in seawater (H O) are deuterium. The atomic mass number of oxygen is 6. About how many kilograms of seawater would be needed per year to provide the hydrogen fuel for fusion reactors to meet the energy needs of the United States? 0. A photon of wavelength.0 x 0 - m strikes a free electron of mass m e that is initially at rest, as shown below left. After the collision, the photon is shifted in wavelength by an amount λ = h/m e c, and reversed in direction, as shown below right. (a) Determine the energy in joules of the incident photon. (b) Determine the magnitude of the momentum of the incident photon. (c) Indicate whether the photon wavelength is increased or decrease by the interaction. Explain your reasoning. (d) Determine the magnitude of the momentum acquired by the electron.

8 Answers to Spring Not-Break Review Assignment. a) 4 m/s b) s c) 3. m. a) x 0 5 Pa b) graph c) negative d) heat engine since the work done by the system occurs at a higher temperature 3. a) 9 x 0 3 N/C d) -9 x 0 3 V b) 9 x 0 3 N/C e) opposite of a) iii. c) f) J 4. a) - + b) 00 V c).3 x 0-0 F d) 8. x 0-6 N, right e) 4. x 0 6 m/s 5. a) all four resistors in series with the battery b) all four resistors in parallel with the battery c) i. 0.8 A ii Watts 6. a) E b) E/B earth c) counterclockwise circular path d) evb earth /m p 7. a). x 0-3 T m b) ± 0.04 V c) i A ii. Counterclockwise with a correct explanation of Lenz s Law. d) any correct method of changing flux 8. a) l b) lf o c) f o d) l/ 9. a) E E E b) f m gcosθ c) (m + m )gsinθ - 3f g d) m g sinθ f m 0. a) 4 Mv o bi) v o bii) right ci).5 v o cii) right d) 0.75 Mv o. a) 4 atm b) 400 m c) 4. x 0 5 N d) m/s e) 50 m f) 45 s. a) i. 300,000 J ii. 4 W b) i..88 m/s ii. explanation using Bernoulli s equation 3. a) 50, 6 V b) 6.0 J c) 0.3 T d) +z-axis 4. a) 30 b) 53 c).9 x 0 8 m/s d) 3. x 0-7 m e) a).6 b) i x 0 4 Hz ii..88 x 0 8 m/s iii. 4.3 x 0-7 m c) i. θ increases ii. straight line through origin with a steeper slope than given line. d) a).5 mm bi) 3.8 x 0-7 m bii) 6 x 0 4 Hz c) the distance between bands decreases 7. a) 0.4 m b) m c) 3, 5, 7 times the answer from (b) + explanation d) i. Y increases + justification ii. Y decreases + justification 8. a) i) 4.5 ev or 7. x 0-9 J ii).6 x 0 6 m/s b).83 x 0-7 m c) 5.56 x 0 4 Hz 9. a) 0.03 u b) 3.46 x 0 - J c) 8.66 x 0 3 d) 8.69 x 0 9 kg 0. a) 9.9 x 0-5 J b) 3.3 x 0-3 kg m/s c) photon wavelength increased because there is a decrease in the momentum of the photon and there is an inverse relationship between photon momentum and wavelength d) 6.0 x 0-3 kg m/s