Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 11, Problem 98P

(a)

To determine

The oscillation frequency of the pendulum.

(a)

Expert Solution
Check Mark

Answer to Problem 98P

The oscillation frequency is 0.133Hz.

Explanation of Solution

Mass of object is 15.0kg  and length of thin wire is 14.0m.

Write the equation for the frequency of Foucault pendulum.

f=12πgL

Here, the frequency of pendulum is f, g is the gravitational acceleration, and L is the length Foucault pendulum.

Conclusion:

Substitute 3.14 for π, 9.80m/s2 for g and 14.0m for L in the above equation to find f.

f=12(3.14)9.80m/s214.0m=(0.159)(0.837s1)=0.133Hz

Therefore, the oscillation frequency is 0.133Hz.

(b)

To determine

The maximum speed of the pendulum.

(b)

Expert Solution
Check Mark

Answer to Problem 98P

The maximum speed is 1.24m/s.

Explanation of Solution

Mass of object is 15.0kg, length of thin wire is 14.0m, and the maximum oscillation angle of pendulum is 6.10°

Write the relation between k and speed of wave.

v=ωA (I)

Here, v is the maximum speed of pendulum,ω is the angular frequency, and A is the amplitude of wave.

Write the equation for ω.

ω=gL (II)

Refer the diagram shown below. Write the relation between A and L.

Physics, Chapter 11, Problem 98P , additional homework tip  1

A=Lsinθ (III)

Here, θ is the maximum angle of oscillation.

Rewrite equation (I) by substituting equations (II) and (III).

v=gLLsinθ=gLsinθ

Conclusion:

Substitute 9.80m/s2 for g, 14.0m for L , and 6.10° for θ in the above equation to find v.

v=(9.80m/s2)(14.0m)(sin6.10°)=(11.71m/s)(0.106)=1.24m/s

Therefore, the maximum speed is 1.24m/s.

(c)

To determine

The maximum tension in the wire.

(c)

Expert Solution
Check Mark

Answer to Problem 98P

The maximum tension is 149N.

Explanation of Solution

Mass of object is 15.0kg, length of thin wire is 14.0m, and the maximum oscillation angle of pendulum is 6.10°

The free body diagram of object is shown below.

Physics, Chapter 11, Problem 98P , additional homework tip  2

Write the Newton’s second law to find the net force.

Fmg=m(v2L)

Here, F is the maximum tension and m is the mass of object.

Rewrite the above equation in terms of F.

F=m(g+v2L)

Conclusion:

Substitute 15.0kg for m, 9.80m/s2 for g, 1.24m/s for v , and 14.0m for L in the above equation to find F.

F=(15.0kg)(9.80m/s2+(1.24m/s)214.0m)=(15.0kg)(9.91m/s2)=149N

Therefore, the maximum tension is 149N.

(d)

To determine

The fundamental frequency of standing wave at the time of maximum tension.

(d)

Expert Solution
Check Mark

Answer to Problem 98P

The fundamental frequency is 16.3Hz.

Explanation of Solution

Mass of object is 15.0kg, Mass of wire is 10.0g length of thin wire is 14.0m, and the maximum oscillation angle of pendulum is 6.10°

Write the equation for the fundamental frequency of wave.

f1=v12L

Here, f1 is the fundamental frequency and v1 is the speed of wave at fundamental frequency.

Write the equation for v.

v=FLmw

Here, mw is the mass of wire.

Rewrite the equation for f1.

f1=12LFLmw=F4lmw

Conclusion:

Substitute 14.0m for L, 149N for F, and 10.0g for mw in the above equation to find F.

f1=149N4(14.0m)(10.0g(103kg1g))=16.3Hz

Therefore, the fundamental frequency is 16.3Hz.

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Chapter 11 Solutions

Physics

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