Midterm Exam #1: Solutions

Transcription

1 Midterm Exam #: Solutions. If m = 3.8ft., convert the speed of sound, v sound = 344 m/s, into units of feet per minute, i.e, ft/min ( min = 60 s ). A).85 0 ft/min ; B) C).75 0 ft/min D) ft/min E) ft/min ft/min Use your factors of : 344 m 3.8 ft 60 s = ft/min, i.e., (D) s m min The next questions refer to the following two position versus time plots describing the motion of two mass-spring combinations. The horizontal scale (time) is the same for each (i.e., each tick is equal to 0. s). Amplitude A Time Amplitude B Time The period of A compared to B is: A) shorter; B) longer; or C) the same. Period = time for one complete oscillation. The horizontal scale is time. Wave A clearly has a longer period. (B). Midterm Exam #, P05, Basic Physics of Sound 9 Sept. 000

2 3. The frequency of A compared to B is: A) higher; B) lower; or C) the same. If A has a period longer than B, and f = ---, then A has a lower frequency than B. T Answer: (B) 4. The amplitude of A compared to B is: A) larger; B) smaller; or C) the same. Amplitude is the maximum value of displacement which is clearly larger for A compared to B. Answer: (A). 5. Suppose a xylophone mallet with a hard-rubber head remains in contact with the wooden bar for only a very short time. During that time, it exerts a force of F = 500 N. If that force is concentrated in a contact area of only 5.0 square millimeters (i.e., A = 5.0 mm ), how much pressure is being exerted on that part of the bar during the time of contact? ( 000 mm = m ). A) 00 N/m ; B) 500 N/m ; 5 C).0 0 N/m ; 6 D).0 0 N/m ; 8 E).0 0 N/m. F 500 N P mm. Many people forgot to square A 5.0 mm = = =.0 0 N/m m the conversion factor properly. There are 000 mm in a meter, but many more square millimeters in a square meter... Answer: (E) Midterm Exam #, P05, Basic Physics of Sound 9 Sept. 000

3 6. The Roadrunner zips forward at a speed of 50 m/s for 000 m, and then instantly slows down to a speed of 40 m/s for the next 3000 m in the same direction. What is his/ her (have you ever wondered?) average speed for the total distance? A) 4. m/s; B) 4.5 m/s; C) 45.0 m/s; D) 47.3 m/s; E) 4.6 m/s. t 000 m = = = 0 s, t 3000 m, 50 m/s = = = 75 s 40 m/s v Average speed m m = = = t t + t = 0 s + 75 s 4.m/s 7. A mass of m = 3.0 kg hanging at the end of a spring lazily oscillates up and down with a period of T =.0 s. What is the spring constant, k, of the spring? A) 37 N/m; B) 59. N/m; C) 474 N/m; D) 4.7 N/m; E) 9.6 N/m. v f k = , rearranging, k = ( π) f m = ( π) ( 0.5 Hz) ( 3.0 kg) = 9.6 N/m, π m Answer: (E) 8. Rita accelerates a violin bow with mass of m = 0. kg from rest to a speed of v = 9.0 m/s in a time of t = 0.5 s. What average force does she apply to the bow during this time? A) 4 N; B) 36 N; C) N; D) 30 N; E) 6.0 N. v v First, acceleration: a i 9.0 m/s 0 m/s = = = = 60 m/s, and F = ma, t 0.5 s so F = ( 0. kg) 60 m/s v f t f ( ) = N, Answer: (C). t i Midterm Exam #, P05, Basic Physics of Sound 9 Sept

4 Position, x [m] Time, t [s] k x x=0 m + x - 9. The graph above is the position versus time plot of the mass-spring combination shown to the right. At what times is the potential energy stored in the spring maximum? A) At times t = 3579,,,, s; B) At times t = 59,, s; C) At times t = 04680,,,,, s; D) At times t = 048,, s; E) At times t = 60,, s. PE = --kx, so PE occurs when, i.e., Answer: (C). Note that since x max x = ± x max is squared, we have to include the times when the spring is compressed too (i.e., when x =. x max Position (m) Time (s) Midterm Exam #, P05, Basic Physics of Sound 9 Sept

5 0. The graph above shows the position versus time plot of a student walking down a hallway. During a certain time interval, the student has negative velocity. The velocity during this time interval is: A) 0.5 m/s; B).0 m/s; C).3 m/s; D).0 m/s; E) 4.0 m/s. Velocity is the slope of the position vs. time plot as given. Taking the straight line segment between 8 and s, rise 4 m 4 m velocity = = slope = =. Don t confuse position t run = s 8 s.0 m/s and time! Answer: (D). I attach a block with mass of m =.0 kg to a spring with a spring constant of k = 50 N/m. I first pull the mass stretching the spring.0 cm beyond its equilibrium position and release it to get it oscillating. I then stop the system completely and pull the spring by 4.0 cm to get it oscillating. In this second case with x max = 4.0 cm, compared to the first case ( =.0 cm ): x max A) the period is longer, speed at equilibrium position is larger; B) the period is longer, speed at equilibrium position is smaller; C) the period is shorter, speed at equilibrium position is larger; D) the period is shorter, speed at equilibrium position is smaller; E) the period is the same, speed at equilibrium position is larger; F) the period is the same, speed at equilibrium position is smaller. This is an example of simple harmonic motion where we learned that the frequency and period are independent of initial amplitude. Also, from energy conservation, PE i + KE i = PE f + KE f. Initially, PE i = --kx and KE i = 0, and if final is at the equilibrium point, PE f = 0, so PE i KE f --kx = ; = --mv. If I increase, then must increase. Answer: (E) f x max v f Midterm Exam #, P05, Basic Physics of Sound 9 Sept

6 Worksheet Midterm Exam #, P05, Basic Physics of Sound 9 Sept

7 Formulae Sheet Conversion Factors: m = 3.8 ft ; in =.54 cm ; mile = 580 ft ; kg =.0 lbs ; hour = 3, 600 s ; liter =, 000 cm 3 ; π radians = 360 ; N = kg m ; kg m J = N m = ; Hz = cycle s s Standard Prefixes: mega M kilo k centi c milli m micro nano n µ s Velocity, speed v = ; Average speed over time interval t : v t v f t f v v Acceleration: a = = i ; t t i = = t x f t f x i t i Newton s Second Law: F = ma; Acceleration due to gravity: g = 9.8 m/s ; Weight: w = mg; Force due to a spring: F = kx F Pressure: P = ; Work: W = Fd = KE ; Conservation of energy: KE + PE = constant A Potential Energy due to Gravity: PE = mgh Potential Energy stored in Spring: PE --kx = ; Kinetic Energy: KE = --mv W E Power: P = ---- = --- t t Midterm Exam #, P05, Basic Physics of Sound 9 Sept

8 Frequency, period: f = --- ; Frequency mass/spring system: f T = π k --- m Motion of Simple Harmonic Oscillator: πt x = x cos max T Midterm Exam #, P05, Basic Physics of Sound 9 Sept