The food that the average American consumes in a day provides 2.0 X 10^3 kcal of energy. How many calories a sec is this? *how to set up work in dimensional analysis*? & *what is "k" in kcal stand for*?
k is 1000, as in
kg, km, etc.
2.0*10^3kcal/day * 1day/86400s * 1000cal/kcal = 23.15 cal/s
Oh, the average American consuming food! Well, that's quite a feast! To figure out how many calories per second that amounts to, let's set up the dimensional analysis.
First, we'll convert the given amount of energy from kilocalories (kcal) to regular calories (cal). "K" in kcal stands for kilo, meaning 1 kcal is equal to 1000 calories.
So, 2.0 X 10^3 kcal (the given energy) is equivalent to 2.0 X 10^3 * 1000 cal (converting kcal to cal).
Now, let's focus on time. Since we want the value in seconds, we'll need to convert it from per day to per second. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Therefore, there are 24 * 60 * 60 = 86,400 seconds in a day.
Finally, to calculate the energy consumed per second, we divide the total energy (in calories) by the number of seconds in a day. So, (2.0 X 10^3 * 1000 cal) / 86,400 sec.
I could just give you the answer, but hey, where's the fun in that? Let me crunch those numbers for you! *sounds of a tiny calculator clicking* Voila! The average American consumes approximately 23.15 calories per second (rounded to two decimal places).
I hope that clears things up, or at the very least, brings a smile to your face!
To find out how many calories are consumed per second, we need to convert kilocalories (kcal) to calories (cal).
To set up the work in dimensional analysis, we will use conversion factors that relate kilocalories to calories.
1 kcal = 1000 cal
Now, let's start by writing down the given information:
Food consumed per day = 2.0 × 10^3 kcal
To convert kcal to cal, we will multiply the given value by the conversion factor.
2.0 × 10^3 kcal × (1000 cal / 1 kcal)
Next, we simplify the expression:
= 2.0 × 10^3 kcal × 1000 cal / kcal
= 2.0 × 10^6 cal
Now we know that the average American consumes 2.0 × 10^6 calories per day. To find the number of calories per second, we will divide this value by the number of seconds in a day.
There are 24 hours in a day, and each hour has 60 minutes. Therefore, there are 24 × 60 = 1440 minutes in a day.
Since each minute has 60 seconds, there are 1440 × 60 = 86,400 seconds in a day.
To find the number of calories per second, we divide the daily calorie intake by the number of seconds in a day:
2.0 × 10^6 cal / 86,400 sec
Calculating this expression will give you the number of calories consumed per second by the average American.
Regarding your second question, the "k" in kcal stands for "kilo," which is a metric prefix meaning thousand. Therefore, one kilocalorie is equal to one thousand calories.
To convert the average American's daily consumption of food in kilocalories (kcal) to calories per second, we need to set up a dimensional analysis.
Dimensional analysis is a method used to convert measurements from one unit to another by canceling out units through appropriate multiplication and division.
To set up the dimensional analysis, we'll use the conversion factor that 1 kilocalorie is equal to 1,000 calories (cal).
Step 1: Write down the given information:
Average daily consumption = 2.0 × 10^3 kcal
Step 2: Write down the conversion factor:
1 kcal = 1,000 cal
Step 3: Set up the conversion using a ratio:
2.0 × 10^3 kcal × (1,000 cal / 1 kcal)
Step 4: Multiply the numbers and divide the units:
= (2.0 × 10^3) × (1,000cal / 1kcal) = 2.0 × 10^6 cal
Now, to find calories per second, you need to know the duration in seconds for which this amount of energy is consumed. Let's assume it is consumed over a span of 24 hours (24 × 60 × 60 seconds).
Step 5: Write down the given information:
Duration = 24 hours = 24 × 60 × 60 seconds = 86,400 seconds
Step 6: Divide the total amount of calories by the duration in seconds:
2.0 × 10^6 cal / 86,400 seconds
Step 7: Calculate the answer:
= 23.1 cal/sec
Therefore, the average American's daily consumption of 2.0 × 10^3 kcal provides approximately 23.1 calories per second.
Now, regarding the "k" in kcal, it stands for kilo, which is a prefix meaning "thousand." So, kcal represents kilocalories, which are commonly used as a unit of energy in nutrition to measure the amount of energy provided by food.