AP Physics – Waves Ain’t Gone, Alas - 4
1. A 7.50 kg ball is thrown. It has an initial velocity of 8.468 m/s. It travels a horizontal distance of 7.3 m
in 1.25 s. Find: (a) The weight of the ball. (b) The initial kinetic energy of the ball. (c) The angle of the
ball’s initial velocity with the horizontal.
(a) w  mg
m

 7.5 kg  9.8 2  
s 

73.5 N
m
1

  7.5 kg   8.468 
2
s

1 2
(b) K  mv
2
2

74.9 J
m
v
x
7.3 m
m
s

 5.84
(c) vx 
cos  x 
46.40

t
1.25 s
s
v 8.468 m
s
2. You are on a train traveling at 55.0 km/h. You approach a bell. The actual frequency of the bell is 725
Hz. What frequency do you hear?
5.84
55
km  1000 m  1 h 
m


  15.28
h  1 km  3600 s 
s
m

345

 v 
s
f ' f 
  725 Hz 
 v  vs 
 345 m  15.28 m
s
s



 


759 Hz
q
dcos q
3. Draw a picture of a pendulum showing its swing. Label the following points:
(a) point of maximum velocity, (b) point of minimum velocity, (c) point where
the potential energy is greatest, (d) point where kinetic energy is greatest, (e) if
the period of the pendulum is 0.750 seconds, what is its length? (f) What is the
speed of the pendulum at the bottom of its swing if the angle that the thing makes at its maximum
displacement is 11.0?
(f)
T  2
L
g
T 2  4 2
L
g
L
2
gT
4 2
m
2

 9.8 2   0.75 s 
s 

4 2
1 2
mv v  2 gh  2 g  d  d cos 
2
m
m

0.225
v  2  9.8 2  0.14 m  0.14 m cos11o

s
s 

(g) mgh 



0.140 m
d
4. A pipe is 18.5 cm long and open on one of its ends. (a) What are the frequencies of the first three
harmonics that resonate in the pipe? (b) What is the wavelength of the third harmonic?
(a) v  f 
f 
m
s

4  0.185 m 
345
v

f3  3  466 Hz  
(b)
v f


466 Hz
f5  5  466 Hz  
1.30 x 103 Hz
m
s

1
2330
s
2330 Hz
345
v
f

0.148 m
5. An FM radio station’s basic frequency has a wavelength of 2.67 m. What is its frequency?
v f
f 
v


m
s
3.0 x 108

2.67 m
1.12 x 108 Hz
6. You have this really hot new car. It has one of the most outstanding sound systems available. Anyway it
can like go faster than sound! So. When you are tooling down the test strip at Mach 2 (twice the speed
of sound), could you hear the stereo? Explain the reasoning for your answer, whatever it is.
7. A frictionless pulley has a light string over the thing attached to two masses as shown.
The first mass, m1, is 5.34 g and the second mass, m2, is 5.39 g. Find (a) the
acceleration of the system and (b) the tension in the string.
(a) m2 g  t  m2 a
t  m1g  m1a
m2 g  m1g  m1a  m2 a
 m  m1 
ag 2
 m1  m2 
m  5.39 g  5.34 g 
 9.8 2
s  5.34 g  5.39 g 

0.0457
m
s2
m2
m1
8. A 52.5 kg crate rests on a surface and has a coefficient of kinetic friction of 0.285. A
rope is attached to it. You pull it sideways exerting a force of 145 N. (a) If the rope makes an angle of
25.0 with the horizontal, what is the acceleration of the crate? (b) How much time to drag it 2.50 m?
Fy  0
n  F sin   mg  0 n  mg  F sin 
(a) Fx  ma
F cos    n  ma
F cos     mg  F sin    ma
145
kg  m
2
a

cos 25.0o   0.285   52.5 kg

52.5 kg
a
s
(b) x 
1 2
at
2
t
2x
a

F cos     mg  F sin  
m
m

o
 9.8 2   145 N sin 25.0 
s 


2  2.50 m 
m

 0.877 2 
s 



2.55 s
0.877
m
s2