A spring with a constant of $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ is lying on the ground with one end attached to a wall. An object with a mass of $8 k g$ $8 kg$ and speed of $6 \frac{m}{s}$ $6 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?

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A spring with a constant of $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ is lying on the ground with one end attached to a wall. An object with a mass of $8 k g$ $8 kg$ and speed of $6 \frac{m}{s}$ $6 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-10-21T02:57:56

$6 m$ $6 m$

Explanation:

Kinetic energy of object $= \frac{m v^{2}}{2}$ $= (mv^2)/2$
$= \frac{8 k g \times {(6 m s^{- 1})}^{2}}{2} = 144 J$ $= (8 kg × (6 ms^-1)^2) / 2 = 144 J$

Potential energy stored in spring $= \frac{k x^{2}}{2}$ $= (kx^2)/2$
$= \frac{8 k g s^{- 2} \times x^{2}}{2} = 4 x^{2} k g . s^{- 2}$ $= (8 kgs^-2 × x^2) / (2) = 4x^2kg.s^-2$

According to law of Conservation of Energy
Total energy of object = Total energy absorbed by spring

$144 J = 4 x^{2} k g . s^{- 2}$ $144 J = 4x^2 kg . s^-2$

$x = \sqrt{\frac{144}{4}} m = \sqrt{36} m = 6 m$ $x = sqrt((144) / 4) m = sqrt(36) m = 6 m$

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A spring with a constant of $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ is lying on the ground with one end attached to a wall. An object with a mass of $8 k g$ $8 kg$ and speed of $6 \frac{m}{s}$ $6 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer

Explanation:

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A spring with a constant of 8kgs28 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 8kg8 kg and speed of 6ms6 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer

Explanation:

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A spring with a constant of $8 \frac{k g}{s^{2}}$ $8 (kg)/s^2$ is lying on the ground with one end attached to a wall. An object with a mass of $8 k g$ $8 kg$ and speed of $6 \frac{m}{s}$ $6 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?