Question

Consider a car of mass $1000\text{kg}$ moving with a speed of $36\text{km/h}$ on a smooth road and colliding with a horizontally mounted spring of spring constant $10{\text{KNm}}^{-1}$. Find the maximum compression of the spring.

• A. $5\text{m}$
• B. $10\text{m}$
• C. $3.16\text{m}$
• D. $7.62\text{m}$

Answer 1

The correct option is C $3.16\text{m}$

Given $\left(v\right)=36\times \frac{5}{18}=10\text{m/s}$
At the ${\text{max}}^m$ compression, $KE$ of car gets completely converted into $PE$ of the spring.
Potential energy of spring, $PE=$ kinetic energy of the car, $KE$

$\frac{1}{2}m{v}^2=\frac{1}{2}k{x}_m^2$
$\Rightarrow \frac{1}{2}\times 1000\times 10\times 10=5\times {10}^4\text{J}=\frac{1}{2}k{x}_m^2$

$\Rightarrow \frac{1}{2}\times 10\times {10}^3{x}_m^2=5\times {10}^4$
$\Rightarrow x_m=3.16\text{m}$