A 1.35-kg ball is tied to a 1.10-m long string is being spun in a vertical circle at a constant speed and with a period of 2.10 s. What is the maximum tension in the string?

T = 13.3 N

Explanation:

In this exercise we use Newton's second law, in the lower birth of the circle the tension and force are opposite, so the tension has its maximum value

          T - W = m a

The acceleration is centripetal

         a = v² / r = w² r

We replace

               T = mg + m w² r

The angular velocity is related to the period

              w = 2π f = 2π / T₀

             T₀ = 2.10 s

             T = m (g + 4π² r / T₀²)

Let's calculate

             T = 1.35 (9.8 + 4π² 1.10 /2.10²)

             T = 13.3 N