Problem 13 - College Physics

Question

\(\cdot\) Compute the number of seconds in (a) an hour, (b) a 24 hour day, and (c) a 365 day year.

Step-by-Step Solution

Answer

3600 seconds in an hour, 86400 seconds in a 24-hour day, and 31536000 seconds in a 365-day year.

Step 1: Calculate Seconds in One Hour

To find the number of seconds in one hour, start by noting that one hour contains 60 minutes, and each minute has 60 seconds. Therefore, the number of seconds in an hour is obtained by multiplying the number of minutes per hour by the number of seconds per minute: \[ 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 3600 \text{ seconds/hour} \]

Step 2: Calculate Seconds in a 24-Hour Day

With the result from step 1, calculate the total number of seconds in a day. There are 24 hours in a day, so multiply the number of seconds in an hour by 24: \[ 3600 \text{ seconds/hour} \times 24 \text{ hours/day} = 86400 \text{ seconds/day} \]

Step 3: Calculate Seconds in a 365-Day Year

Using the number of seconds in a day from step 2, calculate the number of seconds in a year that has 365 days. Multiply the seconds in a day by the number of days in a year: \[ 86400 \text{ seconds/day} \times 365 \text{ days/year} = 31536000 \text{ seconds/year} \]

Key Concepts

Seconds Calculation

Seconds are a fundamental unit of time used in various calculations. To break down time into smaller, more manageable units, we often use seconds. Every minute contains 60 seconds, and similarly, every hour is made up of minutes. This concept of breaking time into smaller parts helps in precise time-tracking and planning.
For any time conversion exercise, identifying the correct factors to multiply for conversion is key. Whether it's convert hours to seconds or days to seconds, knowing the exact number of units per measurement is vital. This understanding makes seconds calculation a straightforward yet essential skill.

Hour to Seconds

When converting hours into seconds, we rely on the understanding that each hour is made up of 60 minutes. Each of these minutes is, in turn, composed of 60 seconds. This relationship allows us to conclude that one hour equals 3600 seconds.

• 60 minutes in an hour
• 60 seconds in each minute

To calculate using these factors, we multiply 60 by 60, resulting in 3600 seconds per hour. This multiplication, where both factors are 60, demonstrates the conversion from a larger unit of time to the smallest standardized unit, the second.

Day to Seconds

A full day, or 24-hour period, can also be broken down into seconds. This process begins with knowing the number of hours in a day and the number of seconds in each of those hours.
By multiplying the 24 hours in a day by the previously calculated 3600 seconds per hour result, one arrives at 86,400 seconds in one day. This calculation ensures an accurate conversion and provides a clear understanding of time passage.
It's interesting to see how these conversions help us measure longer periods in seconds, making complex and detailed schedules possible.

Year to Seconds

Calculating the number of seconds in a year incorporates our previous understanding of days and hours to seconds. A standard year has 365 days, each having 86,400 seconds. Simple multiplication allows us to convert this into the total number of seconds for a year.

• 365 days in a year
• 86,400 seconds in a day

By multiplying these two values, we find that there are 31,536,000 seconds in a year. This calculation illustrates how vast numbers can be managed and comprehended using basic math and time conversion principles.