Physics Exam 4

R4.1.4. A speaker emits sound intensity S. The sound intensity at d1 = 9 m away is I1, equivalent to β1 = 80 dB. We wish to obtain the decibel β2 level at d2 = 18 m away from the speaker, where the sound intensity is I2. A. Setup with an appropriate labeled diagram. b. Obtain I2 in terms of I1. c. Calculate the decibels sound intensity β2 at d2 = 18 m away from the speaker.: The sound intensity I2 at 18 m distance is 0.25(=1/4) times the intensity I1 at 9 m. The decibel level at 18 m from the speaker is 74 dB.

: The sound intensity I2 at 18 m distance is 0.25(=1/4) times the intensity I1 at 9 m. The decibel level at 18 m from the speaker is 74 dB.

R4.1.2. A 4 kg metal sphere, attached to a spring of 100 N/m spring constant, moves harmonically on a horizontal frictionless surface with A = 30 cm amplitude. A. Setup with a completely labeled diagram. b. Calculate the period (T ) of the harmonic motion, the angular speed (ω). c. At t = 0, the ball is at its maximum (+A) position. Write down the velocity as a function of time. Find the maximum speed (v0) of the sphere. Calculate the phase angle θ in degrees at t = 0.7 s, the velocity v at that time and show in a diagram the phase, velocity and the projection of the velocity.

ANSWER: The ball oscillates with 1.3 s period and 5 rad/s "angular speed". The maximum speed of the ball is 1.5 m/s, At t = 0.7 s, the phase is θ = 201º and the velocity of the ball is v = +0.54 m/s.

R4.1.5. A wooden cube of H = 40 cm side and ρc = 0.7×103 kg/m3 density floats on water; the upper and bottom sides of the cube are horizontal. A. Setup with a completely labeled diagram showing the forces acting on the floating cube. b. Calculate the height (h) of the cube below the surface of water.

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R4.1.6. Water flows through a horizontal pipe. At point 1 the cross section is A1, the speed is 12 m/s and the pressure 1.3×105 Pa. At point 2 the cross section is A2 = 2A1. A. Setup with a completely labeled diagram. b. Find the speed v2 of water at point 2. c. Calculate the pressure P2 of water at point 2.

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R4.2.1. A vertical spring stretches 15 cm when a 3 kg mass is hung on its end. Then we take off the 3 kg mass and apply a 70 N downward force to the lower end of the spring. A. Setup with two completely labeled diagrams. b. Calculate the spring constant. c. Calculate the elongation of the spring when stretched by the 70 N force. d. Calculate the elastic potential energy of the spring stretched by the 70 N force.

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R4.2.2. A 450 g mass moves harmonically around a middle point with amplitude 40 cm. The speed of the mass as it passes through the center (ω t = 90°) is 2 m/s. A. Setup with a completely labeled diagrams. b. Calculate the angular velocity ω of the harmonic motion. c. Write down the displacement (x), velocity (v) and acceleration (a) of the mass as functions of time.

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R4.2.3. A string fixed at its ends, has 2 g mass, 80 cm length and 500 N tension. A. Setup with a completely labeled diagram. b. Calculate the speed of the waves on the string. c. How long is the wavelength of its fundamental frequency? Diagram. d. Calculate the fundamental frequency. e. Calculate the frequency of the first overtone.

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R4.2.4. The siren of a train moving at 20 m/s emits a 900 Hz sound that is heard by a prospective passenger that waits on the platform of a station 2 km in front of the incoming train. The speed of sound in air is 340 m/s. A. Setup with a completely labeled diagram. b. Calculate the frequency of the siren heard by the prospective passenger.

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R4.2.5. The top surface of an 80 cm side cube lies horizontally 3 m below the water surface. A. Setup with a completely labeled diagram. b. Calculate the water pressure and force on the top surface of the cube. c. Calculate the water pressure and force on the bottom surface of the cube. d. From the above results obtain the force of buoyancy acting on the cube.

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R4.2.6. A horizontal hose has 6 cm diameter, while the diameter of its nozzle has 2 cm. The water flow through the hose is 1.4 liters per second. A. Setup with a completely labeled diagram showing the cross sections and volumes of water per second flowing through hose and nozzle. b. Calculate the speed of water inside the hose. c. Calculate the speed of water leaving the nozzle.

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R4.3.1. A 0.6 kg metal sphere is pressed against the upper end of a vertical spring of negligible mass. The spring constant is 900 N/m and the spring contracts by 12 cm. A. Setup with two completely labeled diagrams. b. Calculate the maximum height of the metal sphere, above its lowest point, after we release the spring. [g = 9.8 m/s2 ]

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R4.3.2. A 3 kg ball moves harmonically with 1.57 s period. The maximum displacement of the ball from its middle point is 12 cm. A. Setup with a completely labeled diagram. b. Calculate the angular speed of the harmonic motion. c. Write down the displacement, velocity and acceleration of the ball as functions of time. d. Find the maximum force acting on the ball and determine at what points it acts.

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R4.3.3. The length of an organ pipe open at both ends is 4.5 m. The speed of sound in air is 340 m/s. A. Setup with a diagram showing the longest standing sound wave formed inside this pipe. b. Calculate the wavelength of the longest wave formed inside the pipe. c. Calculate the fundamental frequency of the sound radiated by this pipe.

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R4.3.4. A stereo system provides 90 dB till 11 pm and then its volume is increased to output 110 db of sound intensity. A. Setup with a completely labeled diagram. b. Calculate how many times more energy is radiated by the speakers of the stereo system after 11pm.

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R4.3.5. A 4 kg body having volume 1.5 lt is dropped from the surface of a 3 m deep swiming pool. While the body falls through the water, the average force of friction is 12 N. A. Setup with a completely labeled diagram also showing the forces of weight, friction and buoyancy. b. Calculate the force (FB) of buoyancy. c. Write the energy equation when the body has descented h meters below the surface. d. From the energy equation obtain the speed of the stone at the bottom of the pool.

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R4.3.6. A pump compresses water to 2×105 Pa in a pipe that has 5 cm radius. The water rises through the pipe and flows through a 2.5 cm radius horizontal nozzle, 7 m higher where the atmospheric pressure is 1×105 Pa. A. Setup with a completely labeled diagram. b. Write down the continuity of flow equation and the Bernoulli equation relating water pressure, speed, etc, near the pump and at the nozzle and obtain the speed of the water leaving the nozzle. c. Calculate the volume of water flowing through the nozzle in liters per second.

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R4.4.1. A 3 kg mass is attached to a horizontal spring (of negligible mass) and an 80 N force elongates the spring by A = 25 cm. We release the spring and the mass oscillates without friction on a horizontal surface. A. Setup with a completely labeled diagram showing the mass at its greatest displacement A and also at x distance from the center. b. Calculate the spring constant. c. Write down, in algebraic form, the energy equation when the mass is point x. d. From the energy equation obtain the speed of the mass 8 cm from the center. e. From the energy equation obtain the speed of the mass at the center.

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R4.4.2. A 70 cm pendulum has 5º maximum angle of deflection. The bob of the pendulum moves harmonically with amplitude A. A. Setup with a completely labeled diagram. b. Calculate the period (T) of oscillation. c. Calculate the amplitude A the maximum displacement of the bob of the pendulum. d. Calculate the maximum speed v0 of the pendulum's bob from its harmonic motion.

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R4.4.3. An 1.5 g, 80 cm long string vibrates with 400 Hz fundamental frequency.. A. Setup with a diagram showing the longest standing wave formed on the string. b. Calculate the wavelength of the longest standing wave formed on the string. c. Calculate the speed of the waves on the string. d. Calculate the tension (T) of the string

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R4.4.4. A musician hears the first whistle of a boat and determines that it has 880 Hz frequency. He knows that the boat would leave in 5 minutes after the first whistle and that he is 1.5 km away. He starts running toward the port and the whistles of the boat appear to have 900 Hz frequency. The speed of sound in air is 340 m/s. A. Setup with a completely labeled diagram. b. Calculate the speed of the musician. c. Find out whether the musician will reach the boat in time.

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R4.4.5. A body weighs 50 N in air and 36 N when immersed in water. A. Setup with two completely labeled diagrams. b. Write down the force equation inside the water and obtain the force (FB) of buoyancy. c. Calculate the volume (V) and mass (m) of the body.

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R4.4.6.A large tank of water has a 3 cm diameter pipe, 7.3 m below the water surface. Water flows through the pipe, but since it is a large tank the water speed on the surface of the tank is almost zero. A. Setup with a completely labeled diagram. b. Write down the Bernoulli equation relating quantities on the water surface inside the tank and at the water coming out of the pipe. From the above equation obtain the speed the water flows out of the pipe. d. Calculate the mass of water flowing out of the tank per second.

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R4.5.1. A 50 g ball is pressed against the upper end of a vertical spring. The spring constant is 180 N/m and the spring contracts by 7 cm. A. Setup with two completely labeled diagrams. b. Calculate the maximum height (above the neutral height of the spring) the ball reaches after we release the spring.

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R4.5.2. An 80 g mass moves harmonically around a middle point with 12 cm amplitude. The speed of the mass as it passes through the center (ωt = 90°) is 3 m/s. A. Setup the problem with a completely labeled diagram. b. Calculate the angular speed ω of the harmonic motion. c. Using the result above, write down the displacement (x), velocity (v) and acceleration (a) of the mass as functions of time.

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R4.5.3. A string, fixed at its ends, has 3 g mass, 60 cm length and 250 N tension. A. Setup with a labeled diagram and show the standing wave of the fundamental frequency. b. Calculate the speed of the waves on the string. c. How long is the wavelength of its fundamental frequency? d. Calculate the fundamental frequency. e. Calculate the frequency of the first overtone.

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R4.5.4. The horn of a car moving at 30 m/s emits a 750 Hz sound. Helen stands 500 m down the road as the car is approaching. The speed of sound in air is 340 m/s. A. Setup with a labeled diagram and a list of all relevant quantities. b. Calculate the frequency of the sound heard by Helen.

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R4.5.5. One end of a cylindrical horizontal tube filled with water has 5 cm diameter and the other end has 30 cm diameter. We apply an 850 N force on the piston on the narrow end. A. Setup with a completely labeled diagram. b. Calculate the change in pressure in the water due to the action of the 850 N force. c. Calculate the change in the force acting on the wide piston.

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R4.5.6. A horizontal pipe has 8 cm radius and it is connected to another horizontal pipe of 4 cm radius. The water flow through the pipes is 30 lt per second. [103 lt = 1 m3 ] A. Setup with a completely labeled diagram showing the volumes per second of water passing through the two pipes. b. Calculate the speed of water inside the 8 cm radius pipe. c. Calculate the speed of water inside the 4 cm radius pipe.

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R4.6.1. The spring constant of a horizontal spring is 1200 N/m. A 5 kg mass moving at 4 m/s on a horizontal frictionless plane hits and sticks to the free end of the spring. A. Setup with two completely labeled diagrams one before the collision and the other showing the spring at its maximum compression. b. Write in words and formula the relevant energy equation. c. From the above equation obtain the maximum compression of the spring.

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R4.6.2. A 1.5 kg mass attached to a spring moves harmonically about a mid point on a horizontal frictionless plane with 9 cm amplitude and 3 s period. A. Setup with a diagram showing all quantities of harmonic motion. b. Calculate the "angular speed" of the harmonic motion. c. Write down the displacement about the midpoint, the velocity and the acceleration as functions of time. d. Calculate the speed of the mass at 0.75 s.

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R4.6.3. The string of a musical instrument has 70 cm length and 2.3 g mass. When struck, the string creates a fundamental frequency of 400 Hz. A. Setup with a completely labeled diagram. b. Calculate the wavelength of the fundamental frequency and the speed of the waves on the string. c. Calculate the tension of the string.

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R4.6.4. The siren of a police car emits a 770 Hz sound. A standing observer hears the frequency of the siren to be 720 Hz. The speed of sound in air is 343 m/s. A. Setup with a completely labeled diagram. b. Is the car approaching or is it moving away from the observer? Justify your answer. c. Calculate the radial velocity (vs) of the police car relative to the observer. v

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R4.6.5. A plastic cube has 40 cm edge and 2.5×103 kg/m3 density. The cube is initially in air and then it is immersed in water. A. Setup with two completely labeled diagrams showing all quantities and forces. b. Calculate the weight of the cube in air. c. Calculate the weight of the cube in water.

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R4.6.6. A 7 cm radius pipe has a long, 3 cm radius nozzle that delivers 4 lt (4×10−3 m3 ) of water per second. A. Setup with a completely labeled diagram that shows the volumes of water passing through the pipe and the nozzle per second. b. Calculate the speed (vp) of water inside the pipe. c. Calculate the speed (vn) of water as it comes out of the nozzle.

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R4.1.3. A 1.2 m tube of a musical instrument is closed on one end. The speed of sound is 343 m/s. A. Setup with a diagram showing the longest standing sound wave formed in the tube. b. Calculate the wavelength of the longest wave formed in the tube. c. Calculate the lowest sound frequency produced by the instrument.

The longest wavelength of sound formed is λ = 4.8 m, four times the length of the tube. The corresponding frequency is 71.

R4.1.1. A horizontal spring of negligible mass and 750 N/m spring constant is compressed by A = 15 cm and a 0.25 kg mass is placed at its end. The spring is released and pushes the mass along a frictionless horizontal surface. A. Setup with a completely labeled diagram. b. Write in algebraic form the energy equation when the mass is −x distance from the neutral position x0 of the spring. c. Calculate the speed v of the mass when it is −5 cm from the neutral position of the spring. d. Calculate the final speed V of the mass.

The speed of the mass is v = 7.7 m/s at x = −5 cm, while its final speed is V = 8.2 m/s.