Mollie is using springs to hang art projects. She hang a 3.0kg picture on one particular spring and it stretches from 30 cm to 45 cm long. W

Question

Mollie is using springs to hang art projects. She hang a 3.0kg picture on one particular spring and it stretches from 30 cm to 45 cm long. What is the spring constant for that spring? If she hangs a 2 kg picture beneath the first one, how long will the spring get?

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Khang Minh 1 year 2021-07-26T22:11:40+00:00 1 Answers 11 views 0

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    2021-07-26T22:13:18+00:00

    Spring constant, k = 784 N/m

    Distance = 49 cm

    Explanation:

    Given:

    Mass, m₁ = 3 kg

    Distance, x₁ = 30 cm

    Distance, x₂ = 45 cm

    Spring constant, k = ?

    (a)

    When the mass is being stretched at a height then potential energy gets converted to kinetic energy.

    Potential energy = kinetic energy

    [tex]mgh = \frac{1}{2} k(h-x)^2[/tex]

    On substituting the value, we get:

    [tex]3 X 9.8 X 0.3 = \frac{1}{2} X k X (0.45 – 0.3)^2\\ \\8.82 = \frac{1}{2} X k X (0.15)^2\\ \\17.64 = k X 0.0225\\\\k = \frac{17.64}{0.0225}\\ \\k = 784 N/m[/tex]

    (b)

    Total mass, m = 3 kg + 2kg

                           = 5 kg

    Distance, x = ?

    We know:

    Force = mg

    Force on a spring = kx

    [tex]mgh = \frac{1}{2}k (x – h)^2[/tex]

    [tex]5 X 9.8 X 0.3 = \frac{1}{2} X 784 X (x – 0.3)^2\\\\14.7 = 392 (x – 0.3)^2\\\\0.0375 = ( x – 0.3)^2\\\\0.194 = x – 0.3\\\\x = 0.494 m[/tex]

    The spring stretches to 0.494m or 49 cm when a weight of 2kg is added

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