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Sedaia [141]
3 years ago
11

A 45.0-kg person steps on a scale in an elevator. The scale reads 460 n. What is the magnitude of the acceleration of the elevat

or?
Physics
1 answer:
WINSTONCH [101]3 years ago
4 0

Answer:

The magnitude of the acceleration of the elevator is 0.422 m/s²

Explanation:

Lets explain how to solve the problem

Due to Newton's Law ∑ Forces in direction of motion is equal to mass

multiplied by the acceleration

We have here two forces 460 N in direction of motion and the weight

of the person in opposite direction of motion

The weight of the person is his mass multiplied by the acceleration of

gravity

→ W = mg , where m is the mass and g is the acceleration of gravity

→ m = 45 kg and g = 9.8 m/s²

Substitute these values in the rule above

→ W = 45 × 9.8 = 441 N

The scale reads 460 N

→ F = 460 N , W = 441 N , m = 45 kg

→ F - W = ma

→ 460 - 441 = 45 a

→ 19 = 45 a

Divide both sides by 45

→ a = 0.422 m/s²

<em>The magnitude of the acceleration of the elevator is 0.422 m/s²</em>

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Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note
Sophie [7]

(a) 2 Hz

The frequency of the nth-harmonic is given by

f_n = n f_1

where

f_1 is the fundamental frequency

Therefore, the frequency of the third harmonic of the A (f_1 = 440 Hz) is

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while the frequency of the second harmonic of the E (f_1 = 659 Hz) is

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The beat frequency between two harmonics of different frequencies f, f' is given by

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f_B = |1320 Hz - 1318 Hz|=2 Hz

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The fundamental frequency on a string is proportional to the square root of the tension in the string:

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this means that by tightening the string (increasing the tension), will increase the fundamental frequency also*, and therefore will increase also the frequency of the 2nd harmonic.

In this situation, the beat frequency is 4 Hz (four beats per second):

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And since the beat frequency is equal to the absolute value of the difference between the 3rd harmonic of the A-note and the 2nd harmonic of the E-note,

f_B = |f_3-f_2|

and f_3 = 1320 Hz, we have two possible solutions for f_2:

f_2 = f_3 - f_B = 1320 Hz - 4 Hz = 1316 Hz\\f_2 = f_3 + f_B = 1320 Hz + 4 Hz = 1324 Hz

However, we said that increasing the tension will increase also the frequency of the harmonics (*), therefore the correct frequency in this case will be

1324 Hz

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