Question

The American physical chemist Gilbert Newton Lewis (1875-1946) proposed a unit of time called the jiffy. According to Lewis, 1 jiffy is the time it takes light to travel 1 centimeter. (a) If you perform a task in a jiffy, how long does it take in seconds? (b) How many jiffys are in 1 minute? Use the fact that the speed of light is approximately $3.00\times {10}^8\mathrm{m}/\mathrm{s}$.

Short answer

(a) A jiffy is approximately $3.33\times {10}^{-11}$ seconds. (b) There are approximately $1.80\times {10}^{12}$ jiffys in a minute.

Step-by-step solution

Convert distance to meters

First, convert the distance of 1 centimeter to meters. Since there are 100 centimeters in a meter, 1 centimeter is $0.01$ meters.

Calculate time for a jiffy

Using the speed of light $c=3.00\times {10}^8$ meters per second, calculate the time it takes for light to travel 0.01 meters. Using the formula $\text{time}=\frac{\text{distance}}{\text{speed}}$, we get $\text{time}=\frac{0.01}{3.00\times {10}^8}$.

Simplify the calculation

Solving the expression $\frac{0.01}{3.00\times {10}^8}$, we get $3.33\times {10}^{-11}$ seconds. This is the duration of 1 jiffy.

Convert minutes to seconds

Calculate the number of seconds in 1 minute. Since there are 60 seconds in a minute, 1 minute equates to 60 seconds.

Calculate the number of jiffys in a minute

Divide the total seconds in a minute by the seconds per jiffy. So, $\frac{60}{3.33\times {10}^{-11}}\approx 1.80\times {10}^{12}$ jiffys.

Key concepts

Time Conversion

When dealing with problems involving different units of time, it's always important to understand how time conversion works. Each unit of time, such as seconds, minutes, or hours, represents a different magnitude. For example, one minute is equivalent to 60 seconds. This knowledge helps with converting one unit of time to another, which is necessary when solving problems like the one about the jiffy.

In the jiffy problem, we first understand how long a jiffy lasts in seconds. By dividing how long a minute lasts in seconds (60 seconds) by the duration of a jiffy (approximately $3.33\times {10}^{-11}$ seconds), we can see how many jiffys fit into one minute. This conversion allows us to comprehend substantial numbers like $1.80\times {10}^{12}$ jiffys, helping us gauge just how fleetingly brief one jiffy truly is.

Unit of Time

The concept of a 'unit of time' is a standard measure used to quantify the passing of time. Common units include seconds, minutes, hours, and days. Each of these units reflects how human society and science measure and understand the flow of time.

The exercise introduces a more humorous and less common unit: the jiffy. A jiffy is defined simply as the time it takes light to cover a distance of one centimeter. Such creative units help illustrate the relative speed of natural phenomena, in this case, the incredible speed of light. By converting a jiffy into seconds, we can grasp its scale compared to more conventional units, facilitating deeper understanding in physics and other scientific fields.

Physics Problem-Solving

Physics problem-solving involves understanding the principles of physics and using formulas to find solutions to problems. This often includes using formulas to calculate time, speed, distance, or other quantities.

In this exercise, we calculate the time light takes to travel a centimeter. We do this by applying the basic physics formula: $\text{time}=\frac{\text{distance}}{\text{speed}}$. This formula is straightforward, but it's essential for solving many physics problems. It requires both an understanding of the numerical values of speed and distance and a commitment to careful calculation.

Using the speed of light in meters per second ($3.00\times {10}^8$ m/s) and the distance light travels (0.01 meters), reveals the time is a mere $3.33\times {10}^{-11}$ seconds, a fascinatingly minuscule duration.

Metric Conversions

Metric conversions are a vital part of solving physics problems, particularly when dealing with internationally used measurements like meters and centimeters. The metric system is based on powers of ten, simplifying the conversion process between units.

For this exercise, knowing that 100 centimeters make up a meter lets us easily convert 1 centimeter to 0.01 meters. Such conversions serve as the foundational step in calculations involving different metric units.

Accurate metric conversions ensure that measurements stay consistent across calculations, a necessity when working with scientific constants like the speed of light. Making sure all units are compatible is the first step in problem-solving to guarantee the accuracy and reliability of the results.