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Aliun [14]
3 years ago
11

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 54.0 . The expl? After landing on

an unfamiliar planet, a space explorer constructs a simple pendulum of length 54.0 . The explorer finds that the pendulum completes 107 full swing cycles in a time of 132 What is the magnitude of the gravitational acceleration on this planet?
Physics
1 answer:
iogann1982 [59]3 years ago
7 0
<span>We can find the period P of one cycle, and then we can use the period to find the gravitational acceleration g on this planet. P = (132 s) / (107 cycles) = 1.2336 s/cycle The period P is 1.2336 seconds. This means that it takes 1.2336 seconds for the pendulum to swing back and forth one. Now we can use the period P to find the gravitational acceleration g. The equation for the period of a pendulum is as follows: P = 2 pi \sqrt{L/g} P^2 = (4 pi^2) L / g g = (4 pi^2) L / P^2 g = (4)(pi^2)(0.540 m) / (1.2336 s)^2 g = 14.0 m/s^2 The acceleration of gravity on the planet is 14.0 m/s^2.</span>
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Answer:

(a) if she increases the tension in the string is increased by 15%, the fundamental frequency will be increased to 740.6 Hz

(b) If she decrease the length of the the string by one-third the fundamental frequency will be increased to 840 Hz

Explanation:

(a) The fundamental, f₁, frequency is given as follows;

f_1 = \dfrac{\sqrt{\dfrac{T}{\mu}}  }{2 \cdot L}

Where;

T = The tension in the string

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L = The length of the string

f₁ = The fundamental frequency = 560 Hz

If the tension in the string is increased by 15%, we will have;

f_{(1  \, new)} = \dfrac{\sqrt{\dfrac{T\times 1.15}{\mu}}  }{2 \cdot L} = 1.3225 \times \dfrac{\sqrt{\dfrac{T}{\mu}}  }{2 \cdot L}  = 1.3225 \times f_1

f_{(1  \, new)} = 1.3225 \times f_1 = (1 + 0.3225) \times f_1

f_{(1  \, new)} = 1.3225 \times f_1 =\dfrac{132.25}{100} \times 560 \ Hz  = 740.6 \  Hz

Therefore, if the tension in the string is increased by 15%, the fundamental frequency will be increased by a fraction of 0.3225 or 32.25% to 740.6 Hz

(b) When the string length is decreased by one-third, we have;

The new length of the string, L_{new} = 2/3·L

The value of the fundamental frequency will then be given as follows;

f_{(1  \, new)} =  \dfrac{\sqrt{\dfrac{T}{\mu}}  }{2 \times \dfrac{2 \times L}{3} }  =\dfrac{3}{2} \times \dfrac{\sqrt{\dfrac{T}{\mu}}  }{2 \cdot L} = \dfrac{3}{2} \times 560 \ Hz =  840 \ Hz

When the string length is reduced by one-third, the fundamental frequency increases to one-half or 50% to 840 Hz.

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