Question

Smaller mammals use proportionately more energy than larger mammals; that is, it takes more energy per gram to power a mouse than a human. A typical mouse has a mass of 20 g and, at rest, needs to consume 3.0 Cal each day for basic body processes. If a 68 kg human used the same energy per kg of body mass as a mouse, how much energy would be needed each day?

Answer 1

Answer:

10,200 Cal. per day

Explanation:

The mouse consumes 3.0 Cal each day, and has a mass of 20 grams. We can use this data to obtain a ratio of energy consumption per mass

$\frac{3.0 \ Cal}{20 g} = 0.15 \frac{Cal}{g}$.

For the human, we need to convert the 68 kilograms to grams. We can do this with a conversion factor. We know that:

$1 \ kg = 1000 \ g$,

Now, we can divide by 1 kg on each side

$\frac{1 \ kg}{1 \ kg} = \frac{1000 \ g}{1 \ kg}$,

$1 = \frac{1000 \ g}{1 \ kg}$.

Using this conversion factor, we can obtain the mass of the human in grams, instead of kilograms. First, lets take:

$mass_{human} = 68 \ kg$

We can multiply this mass for the conversion factor, we are allowed to do this, cause the conversion factor equals 1, and its adimensional

$mass_{human} = 68 \ kg * \frac{1000 \ g}{1 \ kg}$

$mass_{human} = 68,000 g$

Now that we know the mass of the human on grams, we can multiply for our ratio of energy consumption

$68,000 \ g * 0.15 \frac{Cal}{g} = 10,200 \ Cal$

So, we would need 10,200  Cal per day.