Chapter 6, Problem 9STP

To determine

The tension in the given chain with a mace attached to it.

Answer to Problem 9STP

The tension in the magical chain is $58.622\text{ N}$.

Explanation of Solution

Given:

A warrior swings a mace of 5.6-kgon the end of a massless chain whose length is 86-cm in a horizontal circle above his head such that one revolution takes 1.8 s.

Formula Used:

An object of mass m attached to a string revolving with respect to a center undergoes a centripetal acceleration a. The centripetal tension force associated with this is expressed as,

  ${\text{F}}_T=m{a}_c$

The centripetal acceleration is dependent on the length of the string r and time for one full revolution $T$

  $a_c=\frac{4{\pi }^{2}r}{T^2}$

  

Figure 1

Calculation:

Here, the length of string is given as $r=86-\text{cm}$ and the time for one revolution is $T=1.8\text{ s}$ . Therefore, the centripetal acceleration is calculated as,

  $\begin{array}{c}{a}_c=\frac{4{\pi }^2\times 86\times {10}^{-2}}{{1.8}^2}\\ =10.468{\text{ m/s}}^2\end{array}$

Therefore, the centripetal tension force in the string is given by,

  $\begin{array}{c}{\text{F}}_T=m{a}_c\\ =5.6\times 10.468\\ =58.622\text{ N}\end{array}$

Conclusion:

Therefore, the tension in the string is 58.622 N.