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daser333 [38]
3 years ago
8

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
Physics
1 answer:
IgorC [24]3 years ago
5 0

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 .

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fomenos

To solve this problem we will apply the concepts related to the final volume of a body after undergoing a thermal expansion. To determine the temperature, we will use the given relationship as well as the theoretical value of the volumetric coefficient of thermal expansion of copper. This is, for example to the initial volume defined as V_1, the relation with the final volume as

V_2 = V_1 +0.163\% V_1

V_2 = V_1 +0.00163V_1

V_2 = 1.00163V_1

Initial temperature = 21.1\°C

Let T be the temperature after expanding by the formula of volume expansion

we have,

V_2 = V_1 (1+\gamma \Delta t)

Where \gamma is the volume coefficient of copper 5.1*10^{-5}/C

1.00163V_1 = V_1(1+\gamma(T-21.1\°))

1.00163 = 1+5.1*10^{-5}(T-21.1\°)

0.00163 = 0.000051T-0.0010761

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