A child twirls a 0.15 kg mass attached to the end of a 15 cm long piece of string. He twirls the mass around at 2.4 revolutions per second in a vertical plane. Calculate the tension in the string when the mass is at the top of the circle.

To calculate the tension in the string when the mass is at the top of the circle, we can use the centripetal force formula:

F = (m * v^2) / r

Where:
- F represents the centripetal force
- m represents the mass of the object
- v represents the velocity of the object
- r represents the radius of the circle

First, let's calculate the velocity of the object. Since the object is moving in a circle, its velocity can be found using the formula:

v = 2 * π * r * n

Where:
- π represents the mathematical constant pi (approximately 3.14)
- r represents the radius of the circle
- n represents the number of revolutions per second

Given that the radius of the circle is 15 cm (or 0.15 m) and the number of revolutions per second is 2.4, we can calculate the velocity:

v = 2 * 3.14 * 0.15 m * 2.4 rev/s

Simplifying the equation:

v = 2 * 3.14 * 0.15 m * 2.4 rev/s
v ≈ 2.83 m/s

Now, we can plug the values of mass (0.15 kg), velocity (2.83 m/s), and radius (0.15 m) into the centripetal force formula:

F = (0.15 kg * (2.83 m/s)^2) / 0.15 m

Simplifying the equation:

F = (0.15 kg * 8.009 m^2/s^2) / 0.15 m
F ≈ 8.009 N

Therefore, the tension in the string when the mass is at the top of the circle is approximately 8.009 Newtons.