A car of mass $1000 \mathrm{~kg}$ having a velocity of $10 \mathrm{~ms}^{-1}$ collides a horizontally…
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
$25 \mathrm{~m}$
$15 \mathrm{~m}$
$5 \mathrm{~m}$
$10 \mathrm{~m}$
Solution
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 $\Delta x=5 \mathrm{~m}$