PHYS 2325 University Physics I HOMEWORK PROBLEMS CRN 50394 Chapter 15 Khalid Bukhari HW 15 OSCILLATORY MOTION Hand in your answers in class on scantron on Monday 09 August 2010 1 In an engine a piston oscillates with simple harmonic motion so that its position varies according to the expression p x 5 00 cm cos 2t 6 where x is in centimeters and t is in seconds Find the period of the motion a 1 14 s b 2 14 s c 3 14 s 2 A simple harmonic oscillator takes 12 0 s to undergo five complete vibrations Find the angular frequency in radians per second a 2 62 r s b 1 62 r s c 0 62 r s 3 A piston in a gasoline engine is in simple harmonic motion Taking the extremes of its position relative to its center point as 5 00 cm find the maximum velocity of the piston when the engine is running at the rate of 3 600 rev min a 18 8 m s a 15 5 m s a 11 1 m s 4 A simple pendulum has a mass of 0 250 kg hanging by a string of length of 1 00 m It is displaced through an angle of 15 0 and then released Where will the tension in the string be maximum a at 15 b at 0 5 7 A 0 500 kg object attached to a spring with a force constant of 8 00 N m vibrates in simple harmonic motion with an amplitude of 10 0 cm Calculate a the maximum value of its speed and acceleration b the speed and acceleration when the object is 6 00 cm from the equilibrium position and c the time interval required for the object to move from x 0 to x 8 00 cm 5a a v 40 cm s a 40 cm s2 b v 40 cm s a 160 cm s2 c v 160 cm s a 40 cm s2 6b a v 32 cm s a 40 cm s2 b v 32 cm s a 96 cm s2 c v 32 cm s a 96 cm s2 7c a t 0 232 s b t 0 323 s c t 0 4s 1 PHYS 2325 University Physics I CRN 50394 Khalid Bukhari HW 15 8 11 A 2 00 kg object is attached to a spring and placed on a horizontal smooth surface A horizontal force of 20 0 N is required to hold the object at rest when it is pulled 0 200 m from its equilibrium position the origin of the x axis The object is now released from rest with an initial position of xi 0 200 m and it subsequently undergoes simple harmonic oscillations Find a the force constant of the spring b the frequency of the oscillations and c the maximum speed of the object Where does this maximum speed occur d Find the maximum acceleration of the object 8a 9b 10c 11d a a a a 100 N m 1 51 Hz 1 41 m s 5 m s2 b b b b 200 N m 1 13 Hx 1 61 m s 15 m s2 c c c c 300 N m 0 91 Hz 1 81 m s 10 m s2 12 While riding behind a car traveling at 3 00 m s you notice that one of the car s tires has a small hemispherical bump on its rim as shown in Figure P15 23 If the radii of the car s tires are 0 300 m what is the bump s period of oscillation a 0 528 s b 0 628 s c 0 728 s 13 A simple pendulum is 5 00 m long What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 5 00 m s2 a 3 65 s b 3 85 s c 4 05 s 2 PHYS 2325 University Physics I CRN 50394 Khalid Bukhari HW 15 HOMEWORK PROBLEMS Chapter 16 WAVE MOTION Hand in your answers in class on scantron on Monday 09 August 2010 Starting from 81 on scantron 7 A sinusoidal wave is traveling along a rope The oscillator that generates the wave completes 40 0 vibrations in 30 0 s Also a given maximum travels 425 cm along the rope in 10 0 s What is the wavelength of the wave a b c 0 519 m 0 419 m 0 319 m 8 For a certain transverse wave the distance between two successive crests is 1 20 m and eight crests pass a given point along the direction of travel every 12 0 s Calculate the wave speed a 0 8 m s b 0 6 m s c 0 4 m s 9 A wave is described by y 2 00 cm sin kx t where k 2 11 rad m 3 62 rad s x is in meters and t is in seconds Determine the amplitude wavelength frequency and speed of the wave a b c A 2 0 cm A 4 0 cm A 6 0 cm 2 98 cm 2 00 cm 2 98 cm f 0 576 Hz f 0 777 Hz f 0 576 Hz v 1 72 m s v 1 72 m s v 1 72 m s 4 A seismographic station receives S and P waves from an earthquake 17 3 s apart Assume the waves have traveled over the same path at speeds of 4 50 km s and 7 80 km s Find the distance from the seismograph to the hypocenter of the earthquake a 100 km b 153 km c 184 km 23 A piano string having a mass per unit length equal to 5 00 10 3 kg m is under a tension of 1 350 N Find the speed with which a wave travels on this string a 520 m s b 823 m s c 1040 m s 3 PHYS 2325 University Physics I CRN 50394 Khalid Bukhari HW 15 24 Transverse pulses travel with a speed of 200 m s along a taut copper wire whose diameter is 1 50 mm What is the tension in the wire The density of copper is 8 92 g cm3 a 429 N b 532 N c 631 N 25 An astronaut on the Moon wishes to measure the local value of the free fall acceleration by timing pulses traveling down a wire that has an object of large mass suspended from it Assume a wire has a mass of 4 00 g and a length of 1 60 m and assume a 3 00 kg object is suspended from it A pulse requires 36 1 ms to traverse the length of the wire Calculate gMoon from these data You may ignore the mass of the wire when calculating the tension in it a 0 51 m s2 b 1 64 m s2 c 1 02 m s2 4 PHYS 2325 University Physics I CRN 50394 Khalid Bukhari HW 15 HOMEWORK PROBLEMS Chapter 17 SOUND WAVES Hand …