In Fig, block 1 (mass 2.0 kg) is moving rightward at 10 m/s and block 2 (mass 5.0 kg) is moving rightward at 3.0 m/s. The surface is frictio

Question

In Fig, block 1 (mass 2.0 kg) is moving rightward at 10 m/s and block 2 (mass 5.0 kg) is moving rightward at 3.0 m/s. The surface is frictionless, and a spring with a spring constant of 571 N/m is fixed to block 2. When the blocks collide, the compression of the spring is maximum at the instant the blocks have the same velocity of 5 m/s. Find the maximum compression.

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Ngọc Diệp 4 years 2021-08-02T14:12:50+00:00 1 Answers 17 views 0

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  1. Eirian
    0
    2021-08-02T14:13:59+00:00
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    Answer:

    xmax = 0.65m

    Explanation:

    When the spring is maximum compressed all kinetic energy of both masses will be elastic potential energy of the spring. From there we can take apart xmax. Hence we have

    E_{k1}+E_{k2}=\frac{1}{2}kx_{max}^2

    x_{max}=\sqrt{\frac{1}{k}(m_1v_1^2+m_2v_2^2)}\\x_{max}=\sqrt{\frac{1}{571N/m}[(2.0kg)(10\frac{m}{s})^2+(5.0kg)(3.0\frac{m}{s})^2]}\\\\x_{max}=0.65m

    hope this helps!!

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