57. The pendulum shown in FIGURE P15.57 is pulled to a 10° angle on the left side and released. a. What is the period of this pendulum? b. What is the pendulum's maximum angle on the right side? FIGURE P15.57 12 cm Peg. 12 cm,

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Number 57

WARNING
-17
Twas portt
WW
STINGRE
FA
m
N
16 Tasting W
MA
PEN
●O
11
418 CHAPTER 15 Oscillations
56. | Orangutans can move by brachiation, swinging like a pendu-
BIO lum beneath successive handholds. If an orangutan has arms that
are 0.90 m long and repeatedly swings to a 20° angle, taking one
swing after another, estimate its speed of forward motion in m/s.
While this is somewhat beyond the range of validity of the
small-angle approximation, the standard results for a pendulum
are adequate for making an estimate.
57. The pendulum shown in FIGURE P15.57
is pulled to a 10° angle on the left side and
released.
a. What is the period of this pendulum?
b. What is the pendulum's maximum angle
on the right side?
FIGURE P15.57
12 cm
Peg.
12 cm
58. A uniform rod of mass M and length L swings as a pendulum
on a pivot at distance L/4 from one end of the rod. Find an expres-
sion for the frequency f of small-angle oscillations.
59. Interestingly, there have been several studies using cadavers to
BIO determine the moments of inertia of human body parts, informa-
tion that is important in biomechanics. In one study, the center of
mass of a 5.0 kg lower leg was found to be 18 cm from the knee.
When the leg was allowed to pivot at the knee and swing freely as
a pendulum, the oscillation frequency was 1.6 Hz. What was the
moment of inertia of the lower leg about the knee joint?
60. || A 500 g air-track glider attached to a spring with spring con-
stant 10 N/m is sitting at rest on a frictionless air track. A 250 g
glider is pushed toward it from the far end of the track at a speed of
120 cm/s. It collides with and sticks to the 500 g glider. What are
the amplitude and period of the subsequent oscillations?
61. || A 200 g block attached to a horizontal spring is oscillating with
an amplitude of 2.0 cm and a frequency of 2.0 Hz. Just as it passes
through the equilibrium point, moving to the right, a sharp blow
directed to the left exerts a 20 N force for 1.0 ms. What are the new
(a) frequency and (b) amplitude?
62. || FIGURE P15.62 is a top view of an object of mass m connected
between two stretched rubber bands of length L. The object rests
on a frictionless surface. At equilibrium, the tension in each rub-
her hand is T Find an expression for the frequency of oscilla.
Transcribed Image Text:WARNING -17 Twas portt WW STINGRE FA m N 16 Tasting W MA PEN ●O 11 418 CHAPTER 15 Oscillations 56. | Orangutans can move by brachiation, swinging like a pendu- BIO lum beneath successive handholds. If an orangutan has arms that are 0.90 m long and repeatedly swings to a 20° angle, taking one swing after another, estimate its speed of forward motion in m/s. While this is somewhat beyond the range of validity of the small-angle approximation, the standard results for a pendulum are adequate for making an estimate. 57. The pendulum shown in FIGURE P15.57 is pulled to a 10° angle on the left side and released. a. What is the period of this pendulum? b. What is the pendulum's maximum angle on the right side? FIGURE P15.57 12 cm Peg. 12 cm 58. A uniform rod of mass M and length L swings as a pendulum on a pivot at distance L/4 from one end of the rod. Find an expres- sion for the frequency f of small-angle oscillations. 59. Interestingly, there have been several studies using cadavers to BIO determine the moments of inertia of human body parts, informa- tion that is important in biomechanics. In one study, the center of mass of a 5.0 kg lower leg was found to be 18 cm from the knee. When the leg was allowed to pivot at the knee and swing freely as a pendulum, the oscillation frequency was 1.6 Hz. What was the moment of inertia of the lower leg about the knee joint? 60. || A 500 g air-track glider attached to a spring with spring con- stant 10 N/m is sitting at rest on a frictionless air track. A 250 g glider is pushed toward it from the far end of the track at a speed of 120 cm/s. It collides with and sticks to the 500 g glider. What are the amplitude and period of the subsequent oscillations? 61. || A 200 g block attached to a horizontal spring is oscillating with an amplitude of 2.0 cm and a frequency of 2.0 Hz. Just as it passes through the equilibrium point, moving to the right, a sharp blow directed to the left exerts a 20 N force for 1.0 ms. What are the new (a) frequency and (b) amplitude? 62. || FIGURE P15.62 is a top view of an object of mass m connected between two stretched rubber bands of length L. The object rests on a frictionless surface. At equilibrium, the tension in each rub- her hand is T Find an expression for the frequency of oscilla.
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The solution format looks great but I'm unclear why you put the 10 under pi and for b the answer is theta=7.1. Wanted to know how why 10 is under pi and how theta can equal 7.1

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