Question

a) In a safety test, a car of mass 1000 kg is driven into a brick wall. Its bumperbehaves like a spring (k = 5 x 100 Nm-?) and is compressed by a distance of3 cm as the car comes to rest. Determine the initial speed of the car.​

Answer 1

The initial speed of the car is 1.27 m/min

Explanation:

Mass of the car M = 1000 kg

spring constant of bumper that behaves like a spring k = 500 N/m

It is compressed by 3 cm

Therefore, x = 3 cm = 0.03 m

If the velocity of the car is v then from the question it is clear that the car comes to rest after the compression in spring is 3 cm

At that point, the whole kinetic energy of the car will be converted into potential energy of the spring

Therefore,

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

$\implies Mv^2=kx^2$

$\implies 1000\times v^2=500\times (0.03)^2$

$\implies v^2=\frac{9\times 10^{-4}}{2}$

$\implies v=\frac{3\times 10^{-2}}{\sqrt{2}}$

$\implies v=2.12\times 10^{-2}$ m/s

$\implies v=2.12\times 10^{-2}\times 60$ m/min

$\implies v=1.27$ m/min

Therefore, the initial speed of the car is 1.27 m/min

Hope this answer is helpful.

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