Calculate the tension in qa horizontal string that whirls a 2-kg toy in a circle of radius 2.5 m when it moves at 3 m/s on an icy surface.

To keep the object swirling, it should be that the forces are balanced in the system. The tension in the spring should be equal to the force exerted by the object in the circular motion. So,

Tension = Force by the object in circular motion
    where the force is given by Newton's second law of motion
    F = ma 

Acceleration for a circular motion is the squared of the velocity over  the radius of the motion.
   F = m (v^2) / r

Thus, tension would be

Tension = mv^2 / r
Tension = 2 kg ( 3 m/s)^2 / 2.5 m
Tension = 7.2 kg m/s^2 or 7.2 N

This is what a calorimeter is used for simpler ex, to measure calories in food.