repaso bachillerato- ejercicios
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Review Questions
Simple harmonic motion
1. A particle undergoes SHM with an amplitude of 4.0 mm and angular frequency of 2.0 s -1. At
t 0! the displacement is mm. "rite down the equation gi#ing the displacement forthis motion.
2. A particle undergoes SHM with an amplitude of $.00 cm and an angular frequency of 0.2%0
s-1. At t 0! the #elocity is 1.24 cm s-1
&a' "rite down the equations gi#ing the displacement and #elocity for .this motion.
&(' )alculate the initial displacement.&c' )alculate the *rst time at which the particle is at + 2.00 cm and + -2.00 cm.
3. The graph in Figure shows the displacement of a particle from
a fixed equilibrium position.
a) Use the graph to determine: (i) the period of the motion (ii)
the maximum !elocit" of the particle during an oscillation
and (iii) the maximum acceleration experienced b" the
particle.
b) #n a cop" of the diagram mar$: (i) a point where the
!elocit" is %ero (label this with the letter &) (ii) a point
where the !elocit" is positi!e and has the largest
magnitude (label this with the letter ') and (iii) a point
where the acceleration is positi!e and has the largestmagnitude (label this with the letter ).
4. ,he graph in igure shows the #ariation withdisplacement of the inetic energy of a particle of
mass 0.40g performing SHM. /se the graph todetermine
&a' the total energy of the particle
&(' the ma+imum speed of the particle&c' the amplitude of the motion
%. A particle of mass 0.%0 g undergoes SHM with angular frequency co .0 s-1 andamplitude 3.0 cm. or this particle! determine
a' the ma+imum #elocity
(' the #elocity and acceleration when the particle has displacement 1.% cm and mo#estowards the equili(rium
position from its initial position at + 3.0 cma' the total energy of the motion.
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The simple pendulum
1 State what is meant (y oscillation and simple harmonic motion.
2 State two ways in which an SHM oscillation is dierent from a general oscillation.
3 A (all goes (ac and forth along a hori5ontal 6oor (ouncing o two #ertical walls. 7s themotion an e+ample of an oscillation8 7f yes! is the oscillation simple harmonic8
4 A (all (ounces #ertically o the 6oor. 7s the motion of the (all an e+ample of an oscillation8 7f
yes! is the oscillation simple harmonic8
5 9+plain how you would use a spring of nown spring constant to measure the mass of a (ody
when in a spacecraft in outer space.
6 9+plain why the oscillations of a pendulum are! in general! not simple harmonic. "hat
condition must (e satis*ed for the oscillations to (ecome appro+imately simple harmonic8
7 Show e+plicitly that! if , the period of the motion is gi#en (y
independently of A and ɸ.
8 ,he displacement of a particle e+ecuting SHM is gi#en (y y %.0cos &2t' ! where y is inmillimetres and t is in seconds. )alculate
a the initial displacement of the particle
( the displacement at t = 1.2 s
c the time at which the displacement *rst (ecomes -2.0 mm
d the displacement when the #elocity of the particle is :.0 mm s-1.
9 &a' "rite down an equation for the displacement of a particle undergoing SHM with an
amplitude equal to $.0 cm and a frequency of 14 H5! assuming that at t 0 the
displacement is $.0 cm and the particle is at rest.
&(' ind the displacement! #elocity and acceleration of this particle at a time of 0.02% s.
1A point on a guitar string oscillates in SHM with an amplitude of %.0mm and a frequency of
4:0 H5. ;etermine the ma+imum #elocity and acceleration of this point
Travellin!"wave characteristics
1. A radio station emits at a frequency of 0.$ MH5. "hat is the wa#elength of the wa#es
emitted8
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is polari5ed! partially polari5ed or completely unpolari5ed! e+plaining your answers.
&a',he intensity of the transmitted light is the same no matter what the orientation of the analyser.
&(' ,he intensity of the transmitted light #aries depending on the orientation of theanalyser. At a particular orientation! the transmitted intensity is 5ero.
&c',he transmitted intensity #aries as the orientation #aries! (ut it ne#er (ecomes 5ero.
4% &a' State Malus=s law.
&(' olari5ed light is incident on a polari5er whose transmission a+is maes an Bingle of 2%C with thedirection of the electric *eld of the incident light. )alculate the fraction of the incident lightintensity that gets transmitted through the polari5er.
5% olari5ed light is incident on a polari5er whose transmission a+is maes an angle θ with thedirection of the electric *eld of the incident light. Setch a graph to show the #ariation with angleθ of the transmitted intensity of light.
6% /npolari5ed light of intensity 70 is incident on a polari5er. )alculate! in terms of 70 the intensity oflight transmitted through the polari5er.
7% /npolari5ed light of intensity 70 is incident on a polari5er. ,he transmitted light is incident on asecond polari5er whose transmission a+is is at :00 to that of the *rst. )alculate! in terms of 70 theintensity of light transmitted through the second polari5er.
&nter'erence
1% 9n un e+perimento de interferenciacon dos ranuras! Dstas seencuentran separadas por unadistancia de 0.200 mm! y lapantalla estE a una distancia de1.00 m. Se o(ser#a que la tercerafranFa (rillante &sin contar la franFa(rillante central frente a lasranuras' estE despla5ada .4 mmde la franFa central &*gura '. )alcule la longitud de onda de la lu5 utili5ada.
2% "a#es lea#ing two sources arri#e at point . oint is 12 m from the *rst source and 1:.% mfrom the second. ,he wa#es ha#e a wa#elength of 3 m. "hat is o(ser#ed at 8
03. lanar wa#es of wa#elength 1.0 cm approach an aperture whose opening is also 1.0 cm.;raw the wa#efronts of this wa#e as they emerge through the aperture.
04. Gepeat question 7 for wa#es of wa#elength 1 mm approaching an aperture of si5e 20 cm.
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0%. 7n the corridor shown in igure 4.11 an o(ser#er at point can hear someone at point (ut cannot see them. "hatphysical phenomena may account for this8 How could see 8
0:. ,wo loudspeaers are connected to thesame audio oscillator. An o(ser#er walsalong the straight line Foining the speaers&see igure 4.12'. At a point M halfway(etween the speaers he hears a loudsound. <y the time he gets to point adistance of 2.00 m from M he hears nosound at all. 9+plain how this is possi(le. ind the largest possi(le wa#elength of soundemitted (y the loudspeaers.
0>. A radio station! G! emits radio wa#es of wa#elength 1:00 m which reach a house. H!directly and after re6ecting from a mountain!M! (ehind the house &see igure 4.13'. 7f thereception at the house is #ery poor! what isthe shortest possi(le distance (etween the
house and the mountain8
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