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.

answer: strength i guess

explanation:

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.