1- A 100 kg uniform log hangs by two steel wires, A and B, both of radius 0.205 mm. Initially, wire A
was 2.79 m long and 2.30 mm shorter than wire B. The log is now horizontal. What are the magnitudes
of the forces on it from (a) wire A and (b) wire B? (c) What is the ratio dA /dB?
For the exam problem, FA  500 N ;
FB  480;
d A / dB 
FB
 0.96
FA
2- A string oscillates according to the equation
y = (0.56 cm) sin[( /6.0 cm-1)x] cos[(46 s-1)t].
What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel)
whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the
transverse speed of a particle of the string at the position x = 2.1 cm when t = 1.17 s?
ym 
v
d
u
0.56
cm
2

k

2

46
 276cm / s
 /6

2


 6cm
2k  / 6
y
 46 *  * 0.56 sin(  / 6 * 2.1) sin( 46 *1.17)  38.6cm / s
t
3- A girl is sitting near the open window of a train that is moving at a velocity of 11.3 m/s to the east.
The girl's uncle stands near the tracks and watches the train move away. The locomotive whistle emits
sound at frequency 400 Hz. The air is still. (a) What frequency does the uncle hear? (b) What
frequency does the girl hear? A wind begins to blow from the east at 12.4 m/s. (c) What frequency
does the uncle now hear? (d) What frequency does the girl now hear? (Take the speed of sound to be
343 m/s.)
a- f   f
v
343
 400
 387 Hz
v  vs
343  11.3
b- 400 Hz
c- f   f
d- 400
v  vD
343  12.4
 400
 387.7 Hz
v  vs
343  (12.4  11.3)
4- High-power lasers are used to compress plasma (a gas of charged particles) by radiation pressure.
A laser generating radiation pulses with peak power 1400 MW is focused onto 1.1 mm2 of highelectron-density plasma. Find the pressure exerted on the plasma if the plasma reflects all the light
beams directly back along their paths.
pr 
2I 2P
2 *1400 *106


Pa  8.5 *106 Pa
c
cA 3 *108 *1.1 *10 6
5- A ray of light is perpendicular to the face ab of a prism (n = 1.44). Find the largest value for the
angle φ so that the ray is totally reflected at face ac if the prism is immersed in air.
n1 sin( 1 )  n2 sin(  2 )
1  90  
 2  90
1.44 cos( )  1
  46o
6- An object is 14 cm in front of a convex spherical mirror with focal length of magnitude 17 cm.
What are (a) the radius of curvature of the mirror (including sign), (b) the image distance (including
sign), and (c) the magnification (including sign)?
r  2 f  34cm
(a) and (b) 1 1 1
fp
 14 * 17
  i

 7.7cm
p i
f
p  f 14  (17)
© m=-i/p=7.7/14=0.55
7- A peanut is placed 40 cm in front of a two-lens system: lens 1 (nearer the peanut) has focal length f1
= +20 cm, lens 2 has f2 = -15 cm, and the lens separation is d = 10 cm. For the image produced by lens
2, what are (a) the image distance i2 (including sign), and (b) the lateral magnification?
. (a) Without the diverging lens (lens 2), the real image formed by the converging lens (lens 1) is
located at a distance
1
1
1


 i1  40cm
i1 20 40
to the right of lens 1. This image now serves as an object for lens 2, with p2 = –(40 cm – 10 cm) = –30
cm. So
1
1
1


 i2  30cm
i2  15  30
Thus, the image formed by lens 2 is located 30 cm to the left of lens 2.
(b) The magnification is m = (–i1/p1)  (–i2/p2) = +1.0 > 0, so the image is not inverted.
8- We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.32) so that reflection of light
at wavelength 677 nm is eliminated by interference. What minimum thickness can the coating have to
do this?
2L 
L
m
2 n

4n

m  1,3,5...
677 *10 9 m
 1.28 *10 7 m
4(1.32)
9- How many fringes appear between the first diffraction-envelope minima to either side of the central
maximum in a double-slit pattern if λ = 699 nm, d = 0.169 mm, and a = 39.8 µm? (b) What is the ratio
of the intensity of the third bright fringe to the intensity of the central fringe?
a sin(  )  m
6.99 *10 7
sin(  ) 
 0.018
3.98 *105
d sin(  )  m1
0.000169(0.018)  m1 6.99 * 10  7
m1  4
Total number of bright fringes=2*4+1=9
I  I m cos 2  (
d

sin(  )

a
  sin(  )

sin 

)2
For the third bright fringe:
sin(  ) 
3
d
d 3
( )  cos(3 )  1
 d
a 3

 2.22
 d

I
sin( 0.22) 2
(
)  0.13
Im
0.22
For questions 10 and 11 see the textbook.
12- Water is pumped through the hose shown below, from a lower level to an upper level. Compared
to the water at point 1, the water at point 2:
1- has greater speed and greater pressure
2- has less speed and less pressure
3- has greater speed and less pressure
4- has less speed and greater pressure
5- has greater speed and the same pressure
13- A source emits sound with a frequency of 1000 Hz. It and an observer are moving toward each
other, each with a speed of 100 m/s. If the speed of sound is 340 m/s, the observer hears sound with a
frequency of:
1- 294 Hz
2- 545 Hz
3- 1000 Hz
4- 1830 Hz
5- 3400 H
14- When light travels from medium X to medium Y as shown:
1- both the speed and the frequency decrease
2- both the speed and the frequency increase
3- both the speed and the wavelength decrease
4- both the speed and the wavelength increase
5- both the wavelength and the frequency are unchanged
15- Consider the following four statements concerning a compound microscope:
I.
Each lens produces an image that is virtual and inverted.
II.
The objective lens has a very short focal length.
III.
The eyepiece is used as a simple magnifying glass.
IV.
The objective lens is convex and the eyepiece is concave.
Which two of the four statements are correct?
1- I, II
2- I, III
3- I, IV
4- II, III
5- II, IV
16- In a Young's double-slit experiment, the slit separation is doubled. This results in:
1- an increase in fringe intensity
2- a decrease in fringe intensity
3- a halving of the wavelength
4- a halving of the fringe spacing
5- a doubling of the fringe spacing
17- A diffraction grating of width W produces a deviation θ in second order for light of wavelength λ.
The total number N of slits in the grating is given by:
1- 2Wλ/sinθ
2- (W/λ)sinθ
3- λW/2sinθ
4- (W/2λ)sinθ
5- 2λ/sinθ