Chapter 6, Problem 60A

To determine

Centripetal acceleration of the hammer and tension in the string.

Answer to Problem 60A

Centripetal acceleration of hammer is $a_c=70.98{\text{ m/sec}}^2$ and tension in the string is 496.92 N.

Explanation of Solution

Given :

Mass of the hammer m = 7 kg

Radius of the circle r = 1.8 m

Time taken to complete one revolution t = 1 sec.

Formula used:

Distance covered to complete one revolution.

  $d=2\pi r$

Velocity of an object is,

  $v=\frac{d}{t}$

The centripetal acceleration is

  $a_c=\frac{v^2}{r}$

Centripetal force is given by,

  $F_c=\frac{m{v}^2}{r}$

Calculation:

Distance covered to complete one revolution.

  $\begin{array}{c}d=2\pi r\\ =2\times 3.14\times 1.8\\ =11.304\text{ m}\end{array}$

Velocity of the hammer is given by,

  $\begin{array}{c}v=\frac{d}{t}\\ =\frac{11.304}{1}\\ =11.304\text{ m/sec}\end{array}$

Now, putting the value of v and r to find the centripetal acceleration.

  $\begin{array}{c}{a}_c=\frac{{11.304}^2}{1.8}\\ =70.98{\text{ m/sec}}^2\end{array}$

Tension in string is equal to centripetal force.

Centripetal force is given by,

  $\begin{array}{c}{F}_c=\frac{m{v}^2}{r}\\ =\frac{7\times {11.304}^2}{1.8}\\ =496.92\text{ N}\end{array}$

Conclusion:

Therefore, the centripetal acceleration of hammer is $a_c=70.98{\text{ m/sec}}^2$ and tension in the string is 496.92 N.