Question #103472

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

Expert's answer

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}"

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