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Physics P
Worksheet
14.1b
Worksheet 14.1(b) Pendulums
Pendulums
1. The speed of a grandfather clock is controlled by a swinging pendulum. If the pendulum is currently 15 cm in
length, by how much should the length be changed to shorten the period by 0.04 s?
2. How long must a pendulum be to have a period of 2.3 s on the moon where g = 1.6 m/s2?
3. A clock pendulum has a period of 0.95 s. How much longer will it need to be to have a period of 1.0 s?
4. A simple pendulum made by hanging a mass on a string of length of 0.6 m.
a. What is the period of swing of the pendulum?
b. How much string needs to be added to double the period of oscillation?
c. What happens to the period if the mass on the string is doubled?
5. An astronaut lands on an unknown planet and must determine the value of the gravitational acceleration g
using a variety of survey instruments.
a. One instrument rests on the ground and shoots a ball vertically with a known speed. If the astronaut
measures the time the ball takes to rise from its launch position, and the time the ball takes to fall back to
the launch position, can the astronaut determine the value of g? Why or why not?
b. Another instrument is a simple unmarked weight suspended from a spring with constant k = 22.5 N/m.
Can this instrument be used to determine g? Why or why not?
c. A third instrument consists of a simple pendulum at the end of an arm that is 0.500 m long. The astronaut
counts exactly 47 full swings in 1 min. What is the value of g?
6. A simple pendulum has an arm that is 20 cm long with a 100–g mass suspended from the end. Pulling the
mass 2 cm to one side and releasing it starts the pendulum in motion.
a. What is the amplitude of this pendulum?
b. What is the period of this pendulum?
c. If the arm is lengthened to 50 cm, what happens to the period?
d. If the mass is increased to 500 g, what happens to the period?
e. If the mass is pulled 4.5 cm to one side and released, what happens to the period?
f. A grandfather clock uses a pendulum with a period of 2 s to keep time. If the clock uses a 275–g mass as
a counterweight, how long should the pendulum arm be?
Physics P
1
Worksheet 14.1(b) Pendulums
T  2
l
g
0.15 m
9.8 m/s2
T  0.777s
T  2
T  2
l
l
l
g
gT 2
4 2
9.8 m/s 0.777s - 0.04s
2
2
4 2
l  0.135m
This is 0.015 m or 1.5 cm shorter.
2
T  2
l
l
l
g
gT 2
4 2
1.6 m/s 2.3 s
2
2
4 2
l  0.214 m
3
T  2
l
l
l
g
gT 2
4 2
9.8 m/s 0.95s
2
2
4 2
l  0.224 m
T  2
l
l
l
g
gT 2
4 2
9.8 m/s 1.0 s
2
2
4 2
l  0.248 m
0.248 m – 0.224 m = 0.024 m
Physics P
4a
Worksheet 14.1(b) Pendulums
T  2
l
g
0.6 m
9.8 m/s2
T  1.55 s
T  2
4b
T  2
l
l
l
g
gT 2
4 2
9.8 m/s 2  1.55s
2
2
4 2
l  2 .4 m
You need to add 1.8 m of string
4c
Doubling the mass has no effect on the period.
5a
Yes, a = v/t
5b
No, g = kx/m. Without knowing m you cannot determine g.
5c
60 s
 1.28s/swing
47 swings
T  2
l
g
4 2l
T2
4 2 0.500 m 
g
1.28s 2
g
g  12.1m/s2
6a
6b
The amplitude is 2 cm from where the mass was released.
T  2
l
g
0.2 m
9.8 m/s2
T  0.90 s
T  2
Physics P
6c
Worksheet 14.1(b) Pendulums
T  2
l
g
0.5 m
9.8 m/s2
T  1.42 s
T  2
6d
The period remains the same. Mass does not affect the period.
6e
The period remains the same. Amplitude does not affect the period.
6f
T  2
l
l
g
gT 2
4 2
9.8 m/s 2 s
l
2
4 2
l  0.993 m
2