Problem 11 - College Physics

Question

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

(a) 3600, (b) 86400, (c) 31536000 seconds.

Step 1: Calculating Seconds in an Hour

To find the number of seconds in an hour, we start with the number of minutes in an hour, which is 60, and multiply it by the number of seconds in a minute, which is also 60. So, the calculation is: \[ 60 \times 60 = 3600 \] Thus, there are 3600 seconds in an hour.

Step 2: Calculating Seconds in a Day

Next, we calculate the number of seconds in a 24-hour day by using the number of seconds in an hour we just calculated and multiplying that by 24. The calculation is: \[ 3600 \times 24 = 86400 \] Therefore, there are 86,400 seconds in a 24-hour day.

Step 3: Calculating Seconds in a Year

To find the number of seconds in a non-leap year, we take the number of seconds in a day (86,400) and multiply by the number of days in a year, which is 365. The calculation is: \[ 86400 \times 365 = 31536000 \] Hence, there are 31,536,000 seconds in a 365-day year.

Key Concepts

Calculating Seconds in an Hour

Understanding the conversion of hours to seconds involves knowing two simple key facts: there are 60 minutes in an hour, and each minute contains 60 seconds. By multiplying these values, we can easily determine the total number of seconds in an hour.

Here's how we break it down:

• 1 hour = 60 minutes
• 1 minute = 60 seconds

We multiply the number of minutes in an hour by the number of seconds in a minute: \[ 60 \times 60 = 3600 \]Thus, one hour totals up to 3,600 seconds. This basic understanding is important, as it forms the foundation for further time conversions, such as calculating minutes to seconds. Always remember, an hour is a significant building block in understanding and calculating time intervals in seconds.

Calculating Seconds in a Day

To move on from calculating the number of seconds in an hour to a whole day, we need to consider how many hours make up a full 24-hour day. Simply put, a full day comprises 24 hours. Now, because we already know there are 3,600 seconds in one hour, we can multiply this number by the total number of hours in a day.

Here's the breakdown of the calculation:

• 1 day = 24 hours
• 1 hour = 3,600 seconds (as calculated previously)

The math becomes: \[ 3600 \times 24 = 86400 \]So, a full 24-hour day hosts 86,400 seconds. Converting from hours to a full day is a great exercise in understanding how multiplication helps us scale up from simpler units of time to larger quantities, allowing us to appreciate how time is subdivided into ever-smaller segments.

Calculating Seconds in a Year

When extending our understanding of time from days to years, it's important to recall how many days make up a common year, which is typically 365 days. Given our previous calculation of the number of seconds in a day, transitioning to calculate the total seconds in a year involves a simple multiplication.

Steps to calculate:

• 1 year = 365 days (not accounting for leap years)
• 1 day = 86,400 seconds (from our previous calculation)

Using this information, the calculation is straightforward: \[ 86400 \times 365 = 31536000 \]Thus, there are 31,536,000 seconds in a year with 365 days. This helps us grasp the sheer volume of seconds in longer periods like years, reminding us of the extensive potential each moment holds and how accumulating seconds lead up to significant durations like years.