A spring with a constant of $6$ $6$ $k g s^{- 2}$ $kgs^-2$ is lying on the ground with one end attached to a wall. An object with a mass of $3$ $3$ $k g$ $kg$ and speed of $9$ $9$ $m s^{- 1}$ $ms^-1$ 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 $6$ $6$ $k g s^{- 2}$ $kgs^-2$ is lying on the ground with one end attached to a wall. An object with a mass of $3$ $3$ $k g$ $kg$ and speed of $9$ $9$ $m s^{- 1}$ $ms^-1$ collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2018-03-12T14:01:45

This is a case where kinetic energy $E_{k} = \frac{1}{2} m v^{2}$ $E_k=1/2mv^2$ is converted to spring potential energy $E_{s p} = \frac{1}{2} k x^{2}$ $E_(sp)=1/2kx^2$ .

$E_{k} = \frac{1}{2} m v^{2} = \frac{1}{2} \times 3 \times 9^{2} = 121.5$ $E_k=1/2mv^2=1/2xx3xx9^2=121.5$ $J$ $J$

Rearranging: $x = \sqrt{\frac{2 E}{k}} = \sqrt{\frac{2 \times 121.5}{6}} = 6.36$ $x=sqrt((2E)/k)=sqrt((2xx121.5)/6)=6.36$ $m$ $m$

Explanation:

Here is the rearranging of the spring potential energy equation. I have left off the subscript for simplicity:

$E = \frac{1}{2} k x^{2}$ $E=1/2kx^2$

Multiply both sides by 2:

$2 E = k x^{2}$ $2E=kx^2$

Divide both sides by $k$ $k$ :

$\frac{2 e}{k} = x^{2}$ $(2e)/k=x^2$

Swap the sides:

$x^{2} = \frac{2 E}{k}$ $x^2=(2E)/k$

Take the square root of both sides:

$x = \sqrt{\frac{2 E}{k}}$ $x=sqrt((2E)/k)$

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A spring with a constant of $6$ $6$ $k g s^{- 2}$ $kgs^-2$ is lying on the ground with one end attached to a wall. An object with a mass of $3$ $3$ $k g$ $kg$ and speed of $9$ $9$ $m s^{- 1}$ $ms^-1$ 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 666 kgs^-2kgs−2kgs^-2 is lying on the ground with one end attached to a wall. An object with a mass of 333 kgkgkg and speed of 999 ms^-1ms−1ms^-1 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 $6$ $6$ $k g s^{- 2}$ $kgs^-2$ is lying on the ground with one end attached to a wall. An object with a mass of $3$ $3$ $k g$ $kg$ and speed of $9$ $9$ $m s^{- 1}$ $ms^-1$ collides with and compresses the spring until it stops moving. How much will the spring compress?