Question

to stimulate car accidents auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18 km/h on a smooth road and colliding with a horizontally mounted spring of a spring constant 6.25 10^3N/m. what is the maximum compression of the spring?​

Answer 1

Answer:

The maximum compression in the spring is 2 m

Explanation:

Mass of the car M = 1000 kg

Speed of the car v = 18 km/h = 5 m/s

Spring constant k $=6.25\times 10^3$ N/m

Total kinetic energy of the car

$K=\frac{1}{2}Mv^2$

$\implies K=\frac{1}{2}\times 1000\times 5^2$

$\implies K=12500$ J

After collision this kinetic energy will be converted into Potential Energy of the spring

If maximum compression of the spring is x then

$K=\frac{1}{2}kx^2$

$\implies 12500=\frac{1}{2}\times 6.25\times 10^3\times x^2$

$\implies x^2=\frac{12500\times 2}{6250}$

$\implies x^2=\frac{2500}{625}$

$\implies x^2=4$

$\implies x=\sqrt{4}$

$\implies x=2$ m

Therefore, the maximum compression in the spring is 2 m

Hope this helps.

Answer 2

Hi there....

I have written the steps below...

Hope this helps...