COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Question
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Chapter 1, Problem 93P
To determine

The chair’s frequency for a 75kg astronaut.

Expert Solution & Answer
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Answer to Problem 93P

The chair’s frequency for a 75kg astronaut is 0.46s1_.

Explanation of Solution

Write the given expression for the frequency of the chair.

    fkxmy        (I)

Here, f is the frequency, k is the spring constant, m is the mass, x is the power of k, y is the power of m.

Use the given SI units in equation (I) to solve for the f.

    [M0L0T-1]=[MT-2]x[M]y=[Mx+y][T2x]        (II)

Compare the powers of T on LHS and RHS of equation (II) to solve for x.

    1=2xx=1/2        (III)

Compare the powers of M on LHS and RHS of equation (II) and use equation (III) to solve for y.

    x+y=0y=0x=01/2=1/2        (IV)

Use equation (IV) and (III) in equation (I) to solve for f.

    fkm=2πkm        (V)

Use equation (V) to solve for k.

    k=f2m4π2        (VI)

Write the expression for the m.

    m=mc+ma        (VII)

Here, mc is the mass of the chair, ma is the mass of the astronaut.

Use equation (VII) in (VI) to solve for k.

    k=f2(mc+ma)4π2        (VIII)

Use equation (VII) in (V) to solve for f.

    f=2πkmc+ma        (IX)

Conclusion:

Substitute 0.50s1 for f, 62kg for ma, 10.0kg for mc in equation (VIII) to find k.

    k=(0.50s1)2(62kg+10.0kg)4π2=0.456kg/s2

Substitute 75kg for ma, 0.456kg/s2 for k, 10.0kg for ma in equation (IX) to find f.

    f=2π(0.456kg/s2)(75kg+10.0kg)=0.46s1

Therefore, the chair’s frequency for a 75kg astronaut is 0.46s1_.

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Chapter 1 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

Ch. 1.6 - Prob. 1.8PPCh. 1.6 - Prob. 1.9PPCh. 1.6 - Prob. 1.6CPCh. 1.8 - Prob. 1.10PPCh. 1.9 - Prob. 1.11PPCh. 1.9 - What value of k would you calculate by using only...Ch. 1 - Prob. 1CQCh. 1 - Why must words be carefully defined for scientific...Ch. 1 - Prob. 3CQCh. 1 - Prob. 4CQCh. 1 - Prob. 5CQCh. 1 - Prob. 6CQCh. 1 - Prob. 7CQCh. 1 - Prob. 8CQCh. 1 - Prob. 9CQCh. 1 - Prob. 10CQCh. 1 - Prob. 11CQCh. 1 - Prob. 12CQCh. 1 - Prob. 13CQCh. 1 - Prob. 14CQCh. 1 - Prob. 1MCQCh. 1 - Prob. 2MCQCh. 1 - Prob. 3MCQCh. 1 - Prob. 4MCQCh. 1 - Prob. 5MCQCh. 1 - Prob. 6MCQCh. 1 - Prob. 7MCQCh. 1 - Prob. 8MCQCh. 1 - Prob. 9MCQCh. 1 - Prob. 10MCQCh. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - Prob. 3PCh. 1 - Prob. 4PCh. 1 - Prob. 5PCh. 1 - On Monday, a stock market index goes up 5.00%. On...Ch. 1 - Prob. 7PCh. 1 - Prob. 8PCh. 1 - Prob. 9PCh. 1 - Prob. 10PCh. 1 - Prob. 11PCh. 1 - Prob. 12PCh. 1 - Prob. 13PCh. 1 - Prob. 14PCh. 1 - Prob. 15PCh. 1 - Prob. 16PCh. 1 - Prob. 17PCh. 1 - Prob. 18PCh. 1 - Prob. 19PCh. 1 - Prob. 20PCh. 1 - Prob. 21PCh. 1 - Prob. 22PCh. 1 - Prob. 23PCh. 1 - Prob. 24PCh. 1 - Prob. 25PCh. 1 - Prob. 26PCh. 1 - Prob. 27PCh. 1 - Prob. 28PCh. 1 - Prob. 29PCh. 1 - Prob. 30PCh. 1 - Prob. 31PCh. 1 - Prob. 32PCh. 1 - Prob. 33PCh. 1 - Prob. 34PCh. 1 - Prob. 35PCh. 1 - Prob. 36PCh. 1 - Prob. 37PCh. 1 - Prob. 38PCh. 1 - Prob. 39PCh. 1 - Prob. 40PCh. 1 - Prob. 41PCh. 1 - Prob. 42PCh. 1 - Prob. 43PCh. 1 - Prob. 44PCh. 1 - Prob. 45PCh. 1 - Prob. 46PCh. 1 - Prob. 47PCh. 1 - Prob. 48PCh. 1 - Prob. 49PCh. 1 - Prob. 50PCh. 1 - Prob. 51PCh. 1 - Prob. 52PCh. 1 - Prob. 53PCh. 1 - Prob. 55PCh. 1 - Prob. 56PCh. 1 - Prob. 57PCh. 1 - Prob. 58PCh. 1 - Prob. 59PCh. 1 - Prob. 60PCh. 1 - Prob. 61PCh. 1 - Prob. 62PCh. 1 - Prob. 63PCh. 1 - Prob. 64PCh. 1 - Prob. 65PCh. 1 - Prob. 68PCh. 1 - Prob. 69PCh. 1 - Prob. 70PCh. 1 - Prob. 71PCh. 1 - Prob. 72PCh. 1 - Prob. 73PCh. 1 - Prob. 74PCh. 1 - Prob. 75PCh. 1 - Prob. 76PCh. 1 - Prob. 77PCh. 1 - Prob. 78PCh. 1 - Prob. 79PCh. 1 - Prob. 80PCh. 1 - Prob. 81PCh. 1 - Prob. 82PCh. 1 - Prob. 83PCh. 1 - Prob. 84PCh. 1 - Prob. 85PCh. 1 - Prob. 86PCh. 1 - Prob. 87PCh. 1 - Prob. 88PCh. 1 - Prob. 89PCh. 1 - Prob. 90PCh. 1 - Prob. 91PCh. 1 - Prob. 92PCh. 1 - Prob. 93PCh. 1 - Prob. 94PCh. 1 - Prob. 95PCh. 1 - Prob. 96PCh. 1 - Prob. 97P
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