Answer to Question #103472 in Mechanics | Relativity for Praveen

Question

in a safety test in car of mass 1000 kg is driver into a brick wall its bumper behaves like a spring k is equal to 5 into 10 ki power 6 Newton per metre and is compressed by a distance of 3 cm as the car comes to rest in the initial speed of the car

Answer 1

As the bumper behaves like a spring $k=5\cdot 10^6Nm^{-1}$ and is compressed by a distance of $x=3cm=0.03m$ as the car comes to rest the energy absorb by its is

(1) $E=k\frac{x^2}{2}$

The kinetic energy of the car before brick the wall, is

(2) $E=m\frac{V^2}{2}$ , where $V$ - speed of the car, and $m=1000kg$ is its mass .

As the car comes to rest, all its kinetic energy absorb by bumper, therefor (1) and (2) coincide.

$k\frac{x^2}{2}=m\frac{V^2}{2}$ and $V=x\sqrt{\frac{k}{m}}=0.03m\cdot \sqrt{\frac{5\cdot 10^6Nm^{-1}}{1000kg}}=2.12 ms^{-1}$

Answer: The initial speed of the car is $V=x\sqrt{\frac{k}{m}}=2.12ms^{-1}$