Asoliddisk(r=0.20m,M=0.50kg)issuspendedfromtheendofanL=0.30mlongrod(m=0.30kg,crosssectionalareaof2.0...

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Asoliddisk(r=0.20m,M=0.50kg)issuspendedfromtheendofanL=0.30mlongrod(m=0.30kg,crosssectionalareaof2.0cm^2).Thispendulumissuspendedonafrictionlesspivotontherodattheendoppositetothedisk.Whatisthependulum'speriodforsmallangleoscillations?2)Atanairshow,agirlisstandingbya250mtowerandnoticestheflagontopsuddenlywaving.Then,0.55slater,sheisstartledbyanunexpectedsonicboom.AtwhatMachnumbermustthejethavebeenflyingjudgingbythetimedelaybetweenthetwoevents?3)Therandomnoiselevelofabuzzingmosquitois32dBandthatheardinatypicalclassroomis71dB.Howmanymosquitosarerequiredtomakeanoiselevelequivalenttothatheardin atypicalclassroom?4)For the capacitor network C1=3.00 uF, C2= 1.00 uF, C3=4.00 uF, C4=2.00uF, C5=5.00 uF, C6=10.00uF. Find the net charge, uQ, stored on all capacitors.? (v=20)5)Three charges q1=15mC, q2=8mC and q3=-12mC are assembled from infinitely far away to the locations q1(3,4); q2(-3,1) and q3(2,-1) with the locations indicated in cm as (x,y) for each of the charges.a) At these locations, what is the charge collection’s electric potential energy, U?b)What electric potential energy will a fourth charge q4=4mC and located at the origin with respect to the other three charges experience?c)What voltage , V, would q4 experience due to those other three charges q1,q2,q3?d)What is the potential, V, AT POINT (2,2) Due to all four charges?
	
Document Preview: 1)A solid disk (r=0.20 m, M=0.50 kg) is suspended from the end of an L=0.30m long rod (m=0.30kg, crosssectional area of 2.0 cm^2).This pendulum is suspended on a frictionless pivot on the rod at the end opposite to the disk.What is the pendulum's period for small angle oscillations?2)At an air show, a girl is standing by a 250 m tower and notices the flag on top suddenly waving.  Then, 0.55 s later, she is startled by an unexpected sonic boom.  At what Mach number must the jet have been flying judging by the time delay between the two events?3)The random noise level of a buzzing mosquito is 32dB and that heard in a typical classroom is 71dB. How many mosquitos are required to make a noise level equivalent to that heard in a typical classroom?4)For the capacitor network C1=3.00 uF, C2= 1.00 uF, C3=4.00 uF, C4=2.00uF, C5=5.00 uF, C6=10.00uF.  Find the net charge, uQ, stored on all capacitors.? (v=20)5)Three charges q1=15mC, q2=8mC and q3=-12mC are assembled from infinitely far away to the locations q1(3,4); q2(-3,1) and q3(2,-1) with the locations indicated in cm as (x,y) for each of the charges.a) At these locations, what is the charge collection’s electric potential energy, U?b)What electric potential energy will a fourth charge q4=4mC and located at the origin with respect to the other three charges experience?c)What voltage , V, would q4 experience due to those other three charges q1,q2,q3?d)What is the potential, V, AT POINT (2,2) Due to all four charges?

David · Accepted Answer

1)
For small angle oscillations, the pendulum's time period is given by  
 
 
t
2
t
I
T 2         ----------- (1)
M gd
                            where  T = time period s
                                        I = Inertia of the system kgm  
                                       M  = tot
 
 
 2
al mass of the pendulum kg
                                        g = 9.81 ms
                                        d = distance to the center of the mass(m)

 Given that , (the variables are shown in the fig.)
M 0.50 kg  
m 0.30 kg  
L 0.30m  
R 0.20m  





We have the distance (d) from the pivot to the center of the mass, given by
L
m M(L R)
2
d (2)
m M
 
  
   

 
Substituting the values in the above eq. , we get  
0.30
0.30 0.50(0.30 0.20)
0.045 0.252
d 0.36875m
0.30 0.50 0.80
 
      

 
Inertia of the system is composed of the following three parts: the inertia of the rod about the end, the inertia 
of the disk about its center, and the parallel axis contribution for the disk. Therefore, 
2 2 21 1I mL MR M(L R) (3)
3 2
         
Substituting the values in the above eq. , we get  
2 2 21 1I (0.30)(0.30) (0.50)(0.20) (0.50)(0.30 0.20)
3 2
0.009 0.01 0.125 0.144
   
   
 
The  total mass is  
tM  = m+M= 0.30+0.50=0.80Kg  
Now, Substituting all these values in the eq(1) , we get  
0.144
T 2 1.40157 1.40s (3significant digits)
0.8x9.81x0.36875
   
2) 
Given that , 
altitude ( ) 250m  
timedelay(t) 0.55s


 
2
2 2 2
sound
we have,
M          ----------- (1)
t V
                            where  M = Mach number
                                         = altitude
                                         t = time de


sound
lay
                                        V  = velocity of sound

Here , we take velocity of sound as 340 1ms .

Asoliddisk(r=0.20m,M=0.50kg)issuspendedfromtheendofanL=0.30mlongrod(m=0.30kg,crosssectionalareaof2.0cm^2).Thispendulumissuspendedonafrictionlesspivotontherodattheendoppositetothedisk.Whatisthependulum...

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