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15 March, 21:27

When four people with a combined mass of 315 kg sit down in a 2000-kg car, they find that their weight compresses the springs an additional 0.90 cm. (a) What is the effective force constant of the springs?

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  1. 15 March, 21:30
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    3.43 x 10⁵ N/m

    Explanation:

    M = mass of the car alone = 2000 kg

    m = mass of the four people combined = 315 kg

    x = compression of the spring when there is car alone

    x' = compression of the spring when there is car and four people = x + 0.009

    k = spring constant

    When there is car, the weight of the car is balanced by the spring force and the force equation is given as

    k x = Mg

    k x = (2000) (9.8)

    k x = 19600 eq-1

    When there is car and four people, the weight of the car and four people is balanced by the spring force and the force equation is given as

    k x' = (M + m) g

    k (x + 0.009) = (2000 + 315) (9.8)

    k x + 0.009 k = (2000 + 315) (9.8)

    using eq-1

    19600 + 0.009 k = 22687

    k = 3.43 x 10⁵ N/m
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