A 43 kg person drinks 490 g of milk, which has a "caloric" value of approximately 3.0 kJ/g. If only 16% of the energy in milk is converted to mechanical work, how high (in meters) can the person climb based on this energy intake? [Hint: The work done in ascending is given by mgh, where m is the mass (in kilograms), g the gravitational acceleration (9.8 m/s2), and h the height (in meters.)]

How much energy is in the 490 g milk?

3 kJ/g x 43,000 g x 0.16 = ??
E = mgh. Solve for h.

To calculate the height the person can climb based on the energy intake, we first need to determine the total energy consumed from the milk.

Given:
Person's weight (m) = 43 kg
Amount of milk consumed = 490 g
Caloric value of milk = 3.0 kJ/g

To find the total energy consumed (E), we need to multiply the amount of milk consumed with its caloric value:
E = 490 g * 3.0 kJ/g

Converting grams to kilograms:
E = (490 g / 1000) kg * 3.0 kJ/g

E = 1.47 kg * 3.0 kJ/g

E = 4.41 kJ

Now, we know that only 16% of the energy is converted to mechanical work. We can calculate the work done (W) by multiplying the total energy consumed with the conversion efficiency:
W = 4.41 kJ * 0.16

W = 0.7056 kJ

To find the height (h) that can be climbed, we can use the equation:
W = m * g * h

We rearrange the equation to solve for h:
h = W / (m * g)

Substituting the known values:
h = 0.7056 kJ / (43 kg * 9.8 m/s^2)

Calculating the height:
h = 0.7056 kJ / (421.4 kg•m/s^2)

h ≈ 0.00167 meters

Therefore, based on the energy intake, the person can approximately climb 0.00167 meters.

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