A 10kg box on a horizontal frictionless surface is moving to the right at a speed of 6.0m/s. the box hits and remains attached to one end of a spring of negligible mass whose other end is attached to a wall. as a result, the spring compresses a maximum distance of 0.50 m, and the box oscillates back and forth. the spring does work on the box from the moment the box first hits the spring to the moment the spring first reaches its maximum compression

a) indicate whether the work done by the spring is positive, negative, or zero. explain

b) calculate the magnitude of the work described in part A

c) calculate the spring constant of the spring

d) calculate the magnitude of the maximum acceleration of the box

e) calculate the frequency of the oscillation of the box

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.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards