A spring with a constant of $2 \frac{k g}{s^{2}}$ $2 (kg)/(s^2)$ 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 $5 \frac{m}{s}$ $5 m/s$ 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 $2 \frac{k g}{s^{2}}$ $2 (kg)/(s^2)$ 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 $5 \frac{m}{s}$ $5 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2016-04-19T06:42:09

$10 m$ $10m$

Explanation:

Energy is conserved in this reaction.

Kinetic energy of the object is given by $\frac{1}{2} m v^{2}$ $1/2mv^2$ , where $m$ $m$ is mass and $v$ $v$ is velocity, and potential energy stored in the spring is given by $\frac{1}{2} k x^{2}$ $1/2kx^2$ , where $k$ $k$ is the spring constant and $x$ $x$ is the distance it compresses. If there is always the same amount of energy, then

$\frac{1}{2} m v^{2} = \frac{1}{2} k x^{2}$ $1/2mv^2 = 1/2kx^2$

$therefore mv^2=kx^2$

Rearranging this to make $x$ , the distance of compression, the subject (because the question asks for $x$ ),

$mv^2 = kx^2$

$(mv^2)/k = x^2$

$sqrt((mv^2)/k) = x$ .

Putting in values the question gives us, $k=2(kg)/s^2$ , $m=8kg$ , $v=5m/s$ , then

$x = sqrt((8*5^2)/2)$

$x=sqrt(200/2)$

$x=10m$

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A spring with a constant of $2 \frac{k g}{s^{2}}$ $2 (kg)/(s^2)$ 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 $5 \frac{m}{s}$ $5 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer

Explanation:

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1 Answer

Explanation:

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A spring with a constant of $2 \frac{k g}{s^{2}}$ $2 (kg)/(s^2)$ 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 $5 \frac{m}{s}$ $5 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?