1. A spring is hung from a ceiling, and an object attached to its lower end stre

Question

1. A spring is hung from a ceiling, and an object attached to its lower end stretches the spring by a distance of 5.00 cm from its unstretched position when the system is in equilibrium. If the spring constant is 51.4 N/m, determine the mass of the object.

2. An archer pulls her bowstring back 0.500 m by exerting a force that increases uniformly from zero to 220 N.

(a) What is the equivalent spring constant of the bow?

(b) How much work is done in pulling the bow?

3. A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 24.5 s.

(a) How tall is the tower? (m)

(b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s2, what is the period there? (s)

4. A simple pendulum makes 99 complete oscillations in 2.70 min at a location where g = 9.80 m/s2.

(a) Find the period of the pendulum. (s)

(b) Find the length of the pendulum. (m)

5. The sinusoidal wave shown in the figure below is traveling in the positive x-direction and has a frequency of 14.4 Hz.

(a) Find the amplitude.
cm

(b) Find the wavelength.
cm

(c) Find the period.
s

(d) Find the speed of the wave.
m/s

6. A certain FM radio station broadcasts jazz music at a frequency of 109.5 MHz. (Radio waves are electromagnetic

(a) Find the wave's period.
s

(b) Find its wavelength.
m

7. The distance between two successive minima of a transverse wave is 2.90 m. Five crests of the wave pass a given point along the direction of travel every 15.7 s.

(a) Find the frequency of the wave.
Hz

(b) Find the wave speed.
m/s

8. A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 45.0 vibrations in 29.0 s. Also, a given maximum travels424 cm along the rope in 8.0 s. What is the wavelength?
cm

9. A bat can detect small objects, such as an insect, whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a frequency of50.0 kHz, and if the speed of sound in air is 340 m/s, what is the smallest insect a bat can detect?
mm

10. A cork on the surface of a pond bobs up and down two times per second on ripples having a wavelength of 8.90 cm. If the cork is 14.5 m from shore, how long does it take a ripple passing the cork to reach the shore?
s

11. A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.810 s to reach the opposite tower, 20.0 m away. If a 1 meter length of the rope has a mass of 0.360 kg, find the tension in the tightrope.
N

12. A transverse pulse moves along a stretched cord of length 5.39 m having a mass of 0.160 kg. If the tension in the cord is 14.3 N, find the following.

(a) The wave speed.
m/s

(b) The time it takes the pulse to travel the length of the cord.
s

Explanation / Answer

1.
Kx = mg
mass m = Kx/g = 51.4*0.05/9.8 = 0.2622 kg = 262.2 grams
--------------------------
2.
fromm
F = kx
220 = K*0.5
a) K = 220/0.5 = 440 N/m
b)
W =0.5kx^2 =0.5*440*0.5^2 = 55 J
--------------------------
3)
from T = 2pi*sqrt(l/g)
l = gT^2/4pi^2 = 149.15 m
b)
peroid T = 6.28 *sqrt(149.15/1.67) = 59.3 sec
-----------------------------
4)
a)
T = 2.70*60/99 = 1.636 sec
b)
lenght l = gT^2/4pi^2 = 0.665 m
-------------------------------
5)
Amplirude A=8.26/2 = 4.13 cm
b)
wavelenght L = 2*5.20 = 10.40 cm
c)
perod T = 1/14.4 =0.0694 sec
d)
speed v = fL = 14.4 *0.1040 = 1.4976 m/s
-----------------------------------
6)
a)
peroid T = 1/f = 1/109.5x10^6 = 9.13x10^-9 sec
b)
wavelenght L = 3x10^8/(109.5x10^6) = 2.739 m
------------------------------------
7)
wavelenght L = 2.90 m
time peroid T = 15.7/5 = 3.14 sec
f = 1/T = 1/3.14 = 0.318 hz
b)
wave speed = fL = 0.318*2.90 = 0.923 m/s
-------------------------------------
8)
freq f = 45/29 =1.551 Hz
speed v = 4.24/8 =0.53 m/s
wavelenght L = speed/freq = 0.53/1.551 = 0.3417 m = 34.17 cm
----------------------------------
9)
wavelenght L = speed /freq = 340/50x10^3 =6.8 mm
a bat can detect 6.8 mm
----------------------------------
10)
freq f=2 Hz
wavelenght L = 8.90 cm =0.089 m
speed = fL = 2*0.089 = 0.178 m/s
time t = distance/speed = 14.5/0.178 =81.46 sec
-----------------------------------
11)
speed =20/0.810 = 24.70 m/s
mu = 0.360/1 = 0.360 kg/m
speed = sqrt(T/mu)
Tension T =219.47 N
------------------------------------
12)
lenght l= 5.39 m , mass m=0.160 kg
mass per unit lenght mu = 0.160/5.39 =0.02968 kg/m
a)
speed v = sqrt(T/mu) = sqrt(14.3/0.02968) =21.95 m/s
b)
time t = distance/speed = 5.39/21.95 = 0.245 sec
---------------------------------------
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