A 3 kg block collides with a massless spring of spring constant 98 N/m attached to a wall. The speed of the block was observed to be 1.5 m/s

Question

A 3 kg block collides with a massless spring of spring constant 98 N/m attached to a wall. The speed of the block was observed to be 1.5 m/s at the moment of collision. The acceleration of gravity is 9.8 m/s 2 . How far does the spring compress if the surface on which the mass moves is frictionless

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Calantha 4 years 2021-09-01T00:45:19+00:00 1 Answers 7 views 0

Answers ( )

  1. Eirian
    0
    2021-09-01T00:46:30+00:00
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    Answer: 0.83 m

    Explanation:

    Given

    mass of the block is m=3 kg

    spring constant k=98 N/m

    The Speed at the time of collision is v=1.5 m/s

    Here, the kinetic energy of the block is converted into Elastic potential energy

    \Rightarrow \dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2 \\\\\Rightarrow 3\times 1.5^2=98\times x^2\\\\\Rightarrow x^2=0.6887\\\\\Rightarrow x=0.829\approx 0.83\ m

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