Chapter 2, Problem 30A

Harry the painter swings year after year from his bosun’s chair. His weight is 500 N and the rope, unknown to him, has a breaking point of 300 N. Why doesn’t the rope break when he is supported as shown at the left? One day Harry is painting near a flag-pole, and, for a change, he ties the free end of the rope to the flagpole instead of to his chair as shown at the right. Why did Harry end up taking his vacation early?

To determine

To explain:The reason for not breaking of rope when person H is supported.

Also, the reason for ending up by taking his vacation early.

Answer to Problem 30A

The rope doesn’t break due to the tension on the string as it is below the breaking point of the rope, $T=250\text{ N}<300\text{ N}$ .

Person H falls down, so he end up taking his vacation early.

Explanation of Solution

Given:

The weight of Harry is $W=500\text{ N}$ .

The breaking point of the rope is $300\text{ N}$ .

The given figure is shown below.

  

Formula used:

The expression for the weight is,

  $W=mg$

Here, $m$ is the mass and $g$ is the acceleration due to gravity.

Calculation:

Person H is supported by two strings in the given left Figure.

The tension on the string is,

  $\begin{array}{l}T+T=W\\ 2T=500\text{ N}\\ T=250\text{ N}\end{array}$

The tension on the string is below the breaking point of the rope, $T=250\text{ N}<300\text{ N}$ .

Hence, the rope doesn’t break due to the tension on the string is below the breaking point of the rope, $T=250\text{ N}<300\text{ N}$ .

Person H ties the free end of the rope to the flag pole instead of to his chair. So he is supported by a string in the given right Figure.

The tension on the string is,

  $\begin{array}{l}T=W\\ T=500\text{ N}\end{array}$

The tension on the string is beyond the breaking point of the rope, $T=500\text{ N}>300\text{ N}$ . So the rope breaks and he falls down.