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A car of mass $1000 \mathrm{~kg}$ having a velocity of $10 \mathrm{~ms}^{-1}$ collides a horizontally mounted spring. If the spring constant is $4000 \mathrm{Nm}^{-1}$, then the maximum compression of the spring is
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$5 \mathrm{~m}$
Mass of car, $m=1000 \mathrm{~kg}$
Velocity, $v=10 \mathrm{~m} / \mathrm{s}$
Spring constant, $\mathrm{k}=4000 \mathrm{Nm}^{-1}$
Apply the conservation of energy
$\frac{1}{2} m v^2=\frac{1}{2} k(\Delta x)^2$
$\Delta \mathrm{x}=\sqrt{\frac{\mathrm{mv}^2}{\mathrm{k}}}=\sqrt{\frac{1000 \times 100}{4000}}$
Compression of the spring $\Delta x=5 \mathrm{~m}$
Velocity, $v=10 \mathrm{~m} / \mathrm{s}$
Spring constant, $\mathrm{k}=4000 \mathrm{Nm}^{-1}$
Apply the conservation of energy
$\frac{1}{2} m v^2=\frac{1}{2} k(\Delta x)^2$
$\Delta \mathrm{x}=\sqrt{\frac{\mathrm{mv}^2}{\mathrm{k}}}=\sqrt{\frac{1000 \times 100}{4000}}$
Compression of the spring $\Delta x=5 \mathrm{~m}$
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