4. A merry-go-round has a radius of 2.0 m and a moment of inertia 300 kgm?. A boy of mass 50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is initially at rest, what is the angular velocity after the boy jumps on?

Physics for Scientists and Engineers: Foundations and Connections
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Chapter18: Superposition And Standing Waves
Section: Chapter Questions
Problem 29PQ
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L
Oscillator
m
Figure 2
a. Sketch the shape of the string for the fundamental (lowest possible frequency) standing-
wave mode of vibration of this string. In this case, how many wavelengths fit on the
string?
b. What mass m must be hung from the right end of the string so that the string tension is
what is needed to produce the standing wave that you drew in part (a) at the given 75
Hz oscillation frequency?
c. Sketch the shape of the string for the second harmonic (next possible frequency above
the fundamental) mode of vibration of this string. In this case, how many wavelengths
fit on the string?
d. What mass m must be hung from the right end of the string to produce the standing
wave that you drew in part (c)?
4. A merry-go-round has a radius of 2.0 m and a moment of inertia 300 kgm?. A boy of mass
50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is
initially at rest, what is the angular velocity after the boy jumps on?
5. A sculpture weighing 10,000 N rests on a horizontal surface at the top of a 6.0 m tall vertical
pillar. The pillar's cross-section area is 0.20 m² and it is made of granite with a mass density
of 2700 kg/m'. Find the compressive stress at the cross-section located 3.0 m below the top
of the pillar and the value of the compressive strain of the top 3.0 m segment of the pillar.
6. A block weighing 1.2 N is hung from a spring with a spring constant of 6.0 N/m, as shown
in Figure 3.
Transcribed Image Text:L Oscillator m Figure 2 a. Sketch the shape of the string for the fundamental (lowest possible frequency) standing- wave mode of vibration of this string. In this case, how many wavelengths fit on the string? b. What mass m must be hung from the right end of the string so that the string tension is what is needed to produce the standing wave that you drew in part (a) at the given 75 Hz oscillation frequency? c. Sketch the shape of the string for the second harmonic (next possible frequency above the fundamental) mode of vibration of this string. In this case, how many wavelengths fit on the string? d. What mass m must be hung from the right end of the string to produce the standing wave that you drew in part (c)? 4. A merry-go-round has a radius of 2.0 m and a moment of inertia 300 kgm?. A boy of mass 50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is initially at rest, what is the angular velocity after the boy jumps on? 5. A sculpture weighing 10,000 N rests on a horizontal surface at the top of a 6.0 m tall vertical pillar. The pillar's cross-section area is 0.20 m² and it is made of granite with a mass density of 2700 kg/m'. Find the compressive stress at the cross-section located 3.0 m below the top of the pillar and the value of the compressive strain of the top 3.0 m segment of the pillar. 6. A block weighing 1.2 N is hung from a spring with a spring constant of 6.0 N/m, as shown in Figure 3.
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