Chapter 3, Problem 90A

Interpretation Introduction

Interpretation : The number of minutes that the watch loses in 1 day is to be calculated.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 90A

The number of minutes that the watch loses in 1 day is $3.6\text{min/day}$ .

Explanation of Solution

Given information :

Time lost every minute is $\text{15}\text{sec}$ .

It is known that $\text{1}\text{day}\text{=}24\text{hr}$ , $\text{1}\text{hr}\text{=}60\text{min}$ and $\text{1}\text{min}\text{=}60\text{sec}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The Time lost every minute is given as $\frac{15\text{sec}}{1\text{min}}$ .

The time lost in 1 day is given as

  $\begin{array}{c}\frac{15\text{sec}}{1\text{min}}=\frac{15\cancel{\text{sec}}}{1\cancel{\text{min}}}\left(\frac{60\cancel{\text{min}}}{1\cancel{\text{hr}}}\right)\left(\frac{1\text{min}}{60\cancel{\text{sec}}}\right)\left(\frac{24\cancel{\text{hr}}}{1\text{day}}\right)\left(\because \text{1}\text{day}\text{=}24\text{hr,}\text{1}\text{hr}\text{=}60\text{min},\text{1}\text{min}\text{=}60\text{sec}\right)\\ =3.6\text{min/day}\end{array}$

Conclusion

The number of minutes that the watch loses in 1 day is $3.6\text{min/day}$ .