Chapter 8, Problem 83A

To determine

To explain:The concept behind the pole used by the tightrope walkers that will increases their stability.

Answer to Problem 83A

The use of long pole by the tightrope walkers increases his stability by reducing the angular acceleration to a minimum.

Explanation of Solution

Introduction:

Tightrope walkers are the persons who use to carry a long pole in hand while walking over the rope. The usage of long pole by these tightrope walkers increases their stability and provides ease in walking over the rope without falling down.

Consider a tightrope walker is walking over the rope without carrying a pole in his hand. Then, the gravitational will act on this person in the downward direction.

Due to this gravitational force, a torque will be exerted on the tightrope walker. This torque will induce an angular acceleration in the body tightrope walker which makes the person to tilt on the rope and fall down.

The general expression of the torque experienced by the tightrope walker is,

  $\alpha =\frac{\tau }{I}$

Here, $\alpha$ is the angular acceleration, $I$ is the moment of inertia, and $\tau$ is the torque acting on the tightrope walker.

For the increased stability of the tightrope walker over the rope, the tightrope walker should posses a minimum value of angular acceleration $\left(\alpha \right)$ which can be achieved by decreasing the torque $\left(\tau \right)$ and increasing the moment of inertia $\left(I\right)$ .

Both of these requirements will be satisfied by the usage of a long by the tightrope walkers as follows:

The moment of inertia $\left(I\right)$ is directly proportional to the mass of the tightrope walker and the length of the system. The usage of long pole by the tightrope walker increases both the mass and length of the entire system resulting in an increase in the moment of inertia.

The torque $\left(\tau \right)$ experienced by the tightrope walker walking on the rope depends upon the distance $\left(d\right)$ between the centre of gravity of the person and the rope. Lesser the value of the distance $d$ , lesser will be the torque exerted on the person. The usage of long pole (bowing downward) by the tightrope walker reduces this distance and results in minimized torque on the tight rope walker.

Hence, the use of long pole by the tightrope walkers increases his stability by reducing the angular acceleration to a minimum.

Conclusion:

Thus, the use of long pole by the tightrope walkers increases his stability by reducing his angular acceleration to a minimum.