A 45-kg person drinks 390. g of milk, which has a "caloric" value of approximately 3.0 kJ/g. If only 17% 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.)]

Question

A 45-kg person drinks 390. g of milk, which has a "caloric" value of approximately 3.0 kJ/g. If only 17% 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.)]

Answer 1

I presume the 17% means that work from the milk is 3.0 kJ/g x 390 g x 0.17 = ? kJ of work.

Then plug this into work = mgh as shown in the problem and solve for h = height in meters.

Answer 2

To solve this problem, we first need to calculate the energy intake from drinking the milk, then find the height the person can climb using that energy.

Step 1: Calculate the energy intake from drinking the milk
The person drinks 390 grams of milk, and the caloric value of the milk is approximately 3.0 kJ/g. We can use these values to find the total energy intake.

Energy intake = mass of milk * caloric value
Energy intake = 390 g * 3.0 kJ/g

When calculating with different units, it's important to ensure they are consistent. We need to convert grams to kilograms since the gravitational acceleration is given in m/s².

Energy intake = (390 g / 1000) kg * 3.0 kJ/g
Energy intake = 0.39 kg * 3.0 kJ/g

Step 2: Calculate the work done using the energy intake
We are given that only 17% of the energy is converted to mechanical work. We can calculate the work done using this information.

Work done = energy intake * conversion efficiency
Work done = 0.39 kg * 3.0 kJ/g * 0.17

Step 3: Calculate the height the person can climb
The work done is equal to the potential energy gained by climbing to a certain height. We can use the equation: work done = mgh. In this case, we need to solve for h.

Work done = m * g * h

Rearranging the equation, we find:

h = work done / (m * g)

Let's substitute the calculated values:

h = (0.39 kg * 3.0 kJ/g * 0.17) / (45 kg * 9.8 m/s²)

Simplifying the expression:

h = (0.39 kg * 3.0 kJ/g * 0.17) / (45 kg * 9.8 m/s²)

h ≈ 0.015 m

Therefore, the person can climb to a height of approximately 0.015 meters based on the energy intake from drinking the milk.