Exercise 2.4.6: Suppose you wish to measure the friction a mass of 0.1 kg experiences as it slides along a floor (you wish to find c). You h

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Exercise 2.4.6: Suppose you wish to measure the friction a mass of 0.1 kg experiences as it slides along a floor (you wish to find c). You have a spring with spring constant k 5 N/m. You take the spring, you attach it to the mass and fix it to a wall. Then you pull on the spring and let the mass go. You find that the mass oscillates with frequency 1 Hz. What is the friction

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Thiên Thanh 5 years 2021-08-05T04:48:52+00:00 1 Answers 28 views 0

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  1. diemkieu
    0
    2021-08-05T04:50:28+00:00
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    Answer:

      b = 0.6487 kg / s

    Explanation:

    In an oscillatory motion, friction is proportional to speed,

                   fr = – b v

    where b is the coefficient of friction

    when solving the equation the angular velocity has the form

                   w² = k / m – (b / 2m)²

    In this exercise we are given the angular velocity w = 1Hz, the mass of the body m = 0.1 kg, and the spring constant k = 5 N / m. Therefore we can disperse the coefficient of friction

                 

    let’s call

                   w₀² = k / m

                   w² = w₀² – b² / 4m²

                   b² = (w₀² -w²) 4 m²

    Let’s find the angular velocities

                 w₀² = 5 / 0.1

                 w₀² = 50

                 w = 2π f

                 w = 2π 1

                 w = 6.2832 rad / s

    we subtitute

                   b² = (50 – 6.2832²) 4 0.1²

                   b = √ 0.42086

                    b = 0.6487 kg / s

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