Question

A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.775 s to reach the opposite tower, 20.0 m away. If a 1 meter length of the rope has a mass of 0.300 kg, find the tension in the tightrope. N

Answer 1

Explanation:

The given data is as follows.

      Distance (s) = 20 m

       time (t) = 0.775 s

Also, it is given that mass per 1 meter length (m) = 0.300 kg

Formula to calculate the velocity is as follows.

        Velocity (v) = $\frac{s}{t}$

Putting the given values into the above formula as follows.

              v = $\frac{s}{t}$

                 = $\frac{20 m}{0.775 s}$

                 = 25.80 m/s

We know that,

              v = $\sqrt{\frac{T}{m}}$

Taking square on both the sides, the formula will become as follows.

                      T = $mv^{2}$

                         = $0.3 kg \times 25.80$          

                         = 199.692 N

Therefore, we can conclude that tension in the given tightrope is equal to 199.692 N .