Chapter 6.7, Problem 12CFU

To determine

To find the downward force.

Answer to Problem 12CFU

  $715.4N$

Explanation of Solution

Given:

The mass of the child is $73$ kilograms.

Calculation:

Force is equal to mass $\times$ acceleration

  $\begin{array}{l}F=ma\\ F=73\times 9.8\\ F=715.4N\end{array}$

To determine

To write the equation that represents the tension on the rope as the child swings back and forth.

Answer to Problem 12CFU

  $T=715.4\cos \theta$

Explanation of Solution

Given:

The following is the given figure-

Calculation:

The equation for the tension will be

  $\begin{array}{l}T=mg\cos \theta \\ T=715.4\cos \theta \end{array}$

To determine

To graph the equation for $-\frac{\pi }{2}\le x\le \frac{\pi }{2}$ .

Answer to Problem 12CFU

  $T=715.4\cos \theta$

Explanation of Solution

Given:

The following is the given figure-

Calculation:

The equation for the tension will be

  $\begin{array}{l}T=mg\cos \theta \\ T=715.4\cos \theta \end{array}$

The following is the graph-

To determine

To find the least amount of tension on the rope.

Answer to Problem 12CFU

  $0$

Explanation of Solution

Given:

The following is the given figure-

Calculation:

The equation for the tension will be

  $\begin{array}{l}T=mg\cos \theta \\ T=715.4\cos \theta \end{array}$

The least amount of tension will be $0$ if the angle is ${90}^{\circ }$

To determine

To find the impact if the child swings higher and higher.

Answer to Problem 12CFU

  $0$

Explanation of Solution

Given:

The following is the given figure-

Calculation:

As the child swings higher, the angle gets greater and the vertical force from the rope gets less and less creating less tension in the rope.