A spring with a constant of $\frac{6}{5} \frac{k g}{s^{2}}$ $6/5 (kg)/s^2$ is lying on the ground with one end attached to a wall. An object with a mass of $\frac{3}{5} k g$ $3/5 kg$ and speed of $\frac{5}{4} \frac{m}{s}$ $5/4 m/s$ 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 $\frac{6}{5} \frac{k g}{s^{2}}$ $6/5 (kg)/s^2$ is lying on the ground with one end attached to a wall. An object with a mass of $\frac{3}{5} k g$ $3/5 kg$ and speed of $\frac{5}{4} \frac{m}{s}$ $5/4 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2018-03-02T15:07:33

$\frac{5 \sqrt{2}}{8} m$ $(5 sqrt(2))/8 "m"$

Explanation:

Kinetic energy of object = Energy stored in spring

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

$x = v \sqrt{\frac{m}{k}} = \frac{5}{4} m/s \sqrt{\frac{\frac{3}{5} kg}{\frac{6}{5} {kg/s}^{2}}} = \frac{5}{4 \sqrt{2}} m = \frac{5 \sqrt{2}}{8} m$ $x = vsqrt(m/k) = 5/4 "m/s"sqrt((3/5"kg")/(6/5 "kg/s"^2)) = 5/(4sqrt(2)) "m" = (5sqrt(2))/8 "m"$

Answer 2 · 2018-03-02T15:08:32

The compression is $= 0.88 m$ $=0.88m$

Explanation:

Mass of the object is $m = \frac{3}{5} k g$ $m=3/5kg$

Speed of the object is $v = \frac{5}{4} m s^{- 1}$ $v=5/4ms^-1$

The kinetic energy of the object is

$K E = \frac{1}{2} m v^{2} = \frac{1}{2} \cdot \frac{3}{5} \cdot {(\frac{5}{4})}^{2} = 0.46875 J$ $KE=1/2mv^2=1/2*3/5*(5/4)^2=0.46875J$

This energy will be stored in the spring

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

The spring constant is $k = \frac{6}{5} k g s^{- 2}$ $k=6/5kgs^-2$

Let the compression of the spring be $= x m$ $=xm$

Therefore,

$0.46875 = \frac{1}{2} \cdot \frac{6}{5} \cdot x^{2}$ $0.46875=1/2*6/5*x^2$

$x^{2} = \frac{5 \cdot 0.46875}{3} = 0.78 m^{2}$ $x^2=(5*0.46875)/3=0.78m^2$

The compression of the spring is

$x = \sqrt{0.78} = 0.88 m$ $x=sqrt0.78=0.88m$

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A spring with a constant of 65kgs26/5 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 35kg3/5 kg and speed of 54ms5/4 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

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