10.3. Simple Pendulum http://www.ck12.org
pendulum.
Illustrative Example 1
a. What is the period of a simple pendulum of length 40.0 cm?
Answer:SinceL= 40. 0 cm→ 0. 400 m, the period isT= 2 π
√
L
g=T=^2 π√
0. 400
9. 81 =^1.^269 →^1.^27 sb. How long of a string would be necessary for a pendulum with a period of 2.00 s? (A simple pendulum with the
period of two second is sometimes referred to as a “seconds pendulum,” since the time between the extremes of its
motion is one second.)
Answer:The period is given asT= 2. 00 s
→T= 2 π
√
L
g→^2.^00 =^2 π√
L
9. 81 →L=( 4. 00 )( 9. 81 )
4 π^2 =^0.^9940 m, almost one meter!c. How long would a “seconds pendulum” have to be on Mars? The gravitational acceleration at the Martian surface
is 0.38 that of Earth.
Answer:Let us writegmars= 0. 38 gearth= 0. 38
(
- (^81) sm 2
)
= 3. 728 ms 2→T= 2 π√
L
gmars→ 2. 00 = 2 π√
L
3. 728
→L=
( 4. 00 )( 3. 728 )
4 π^2= 0. 3777 → 0. 378 mNotice that the length of the pendulum must be shorter than that on Earth. Does this seem reasonable? Since the
gravity on Mars is smaller than on Earth, identical pendulums will swing slower on Mars than on Earth. In order for
the period to remain 2.00 s, the length of the pendulum on Mars will need to be smaller.
See if you can show thatLmars=ggmarsearthLearth.
http://phet.colorado.edu/en/simulation/pendulum-lab
Check Your Understanding
1a. If the length of a simple pendulum is doubled, the original periodTof the pendulum will:
a. Remain the same
b. be somewhere betweenTand 2T
c. be 2T
d. be 4T
Answer:The correct answer is B. Remember that the periodTis proportional to the square root of the pendulum’s
lengthL. That is,T∝
√
L.
What answer above would be correct if the length of the pendulum had been four times greater?
(Answer:C)
1b. If the mass of the pendulum bob is doubled the periodT, the pendulum will:
a. Remain the same
b. be somewhere betweenTand 2T
c. be 2T
d. be 4T