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garri49 [273]
3 years ago
12

What must be the length of a simple pendulum if its oscillation frequency is to be equal to that of an air-track glider of mass

0.250 kg attached to a spring of force constant 9.75 N/m
Physics
1 answer:
Anvisha [2.4K]3 years ago
8 0

Answer:

the length of the simple pendulum is 0.25 m.

Explanation:

Given;

mass of the air-track glider, m = 0.25 kg

spring constant, k = 9.75 N/m

let the length of the simple pendulum = L

let the frequency of the air-track glider which is equal to frequency of simple pendulum = F

The oscillation frequency of air-track glider is calculated as;

F = \frac{1}{2\pi } \sqrt{\frac{k}{m} } \\\\F = \frac{1}{2\pi } \sqrt{\frac{9.75}{0.25} } \\\\F = 0.994 \ Hz

The frequency of the simple pendulum is given as;

F = \frac{1}{2\pi} \sqrt{\frac{g}{l} } \\\\2\pi(F) = \sqrt{\frac{g}{l} } \\\\2\pi (0.994) = \sqrt{\frac{9.8}{l} } \\\\6.2455 = \sqrt{\frac{9.8}{l} } \\\\(6.2455)2 = \frac{9.8}{l} \\\\39.006 = \frac{9.8}{l} \\\\l = \frac{9.8}{39.006} \\\\l = 0.25 \ m

Thus, the length of the simple pendulum is 0.25 m.

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Answer:

1. It won't break

2. 0.5 squared meters

Explanation:

1. Pressure (P) is force (F) exerted over an area(A). Greater the force or smaller the area, the pressure will be greater. This is presented by an equation:

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P = 400N / 18m^2

P = 22.2 N/m^2 (N/m^2 is the same unit as Pascal)

So, the table can withstand 250 Pa of pressure, the object exerts only 22.2 Pa, which means that the glass table won't break.

2. Again, we need to know the equation that connects the force and the pressure, and that is:

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In this case, we have both the force and the pressure, and we want to find the surface of the area. From the previous equation, area can be found as:

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A = 20N / 40Pa (N/m^2)

A = 0.5 m^2

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