calculate the tension in a horizontal string that whirls a 2kg toy in a circle of radius 2.5 meters when it moves 3m/s on icy surface​

The tension in the horizontal string is 7.2 N

Explanation:

With the assumption that the ice surface has no friction, the tension in the horizontal string is equal to the centripetal force, 'F', acting on the string to keep it in circular motion

Where;

m = The mass of the object in the circular

v = The tangential velocity of the object

r= The radius of the circle through whose path the object is moved

The given parameters are;

The mass of the toy that is whirled in a circle by the string, m = 2 kg

The radius of the circle the toy's path turns, r = 2.5 meters

The velocity of the toy at the instant the tension is sought, v = 3 m/s

Therefore, we get;

The centripetal force, F = 7.2 N = The tension in the horizontal string

∴ The tension in the horizontal string = 7.2 N.

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.

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.