A spring is 20cm long is stretched to 25cm by a load of 50N. What will be its length when stretched by 100N. assuming that the elastic limit

Question

A spring is 20cm long is stretched to 25cm by a load of 50N. What will be its length when stretched by 100N. assuming that the elastic limit is not reached

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Gerda 5 years 2021-08-23T18:08:08+00:00 1 Answers 335 views 2

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  1. nguyetanh
    0
    2021-08-23T18:10:02+00:00
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    Answer:

    Final Length = 30 cm

    Explanation:

    The relationship between the force applied on a string and its stretching length, within the elastic limit, is given by Hooke’s Law:

    F = kΔx

    where,

    F = Force applied

    k = spring constant

    Δx = change in length of spring

    First, we find the spring constant of the spring. For this purpose, we have the following data:

    F = 50 N

    Δx = change in length = 25 cm  – 20 cm = 5 cm = 0.05 m

    Therefore,

    50 N = k(0.05 m)

    k = 50 N/0.05 m

    k = 1000 N/m

    Now, we find the change in its length for F = 100 N:

    100 N = (1000 N/m)Δx

    Δx = (100 N)/(1000 N/m)

    Δx = 0.1 m = 10 cm

    but,

    Δx = Final Length – Initial Length

    10 cm = Final Length – 20 cm

    Final Length = 10 cm + 20 cm

    Final Length = 30 cm

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