a 1200-kg car rolling on a horizontal surface has speed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?

The stiffness constant of the spring is 80831.191 newtons per meter.

Explanation:

Given that all non-conservative forces are negligible, by the Principle of Energy Conservation we get that initial translational kinetic energy of the car is turned into final elastic potential energy of the spring. That is:

(1)

Where:

- Final elastic potential energy of the coiled spring, measured in joules.

- Initial translational kinetic energy, measured in joules.

By definitions of elastic potential and translational kinetic energies we expand  (1):

(1b)

Then, we clear the stiffness constant within the expression:

Where:

- Mass of the car, measured in kilograms.

- Initial speed of the car, measured in meters per seconds.

- Final deformation of the coiled spring, measured in meters.

If we know that , and , then the stiffness constant of the spring is:

The stiffness constant of the spring is 80831.191 newtons per meter.

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.