A 51 kg person drinks 270. g of milk, which has a "caloric" value of approximately 3.0 kJ/g. If only 15% 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 51 kg person drinks 270. g of milk, which has a "caloric" value of approximately 3.0 kJ/g. If only 15% 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

Well, it seems we have a person who's looking to turn milk into mountains! Let's do some math and see how high they can climb based on their milk intake.

First, we need to calculate the total energy intake from the milk. The person drank 270 g of milk, and each gram has a caloric value of 3.0 kJ/g. So, the total energy intake is:

270 g * 3.0 kJ/g = 810 kJ

Now, we're told that only 15% of this energy can be converted to mechanical work. So, let's calculate how much energy that is:

810 kJ * 0.15 = 121.5 kJ

Now that we have the energy, let's calculate the height the person can climb. We'll use the formula mgh, where m is the mass (51 kg) and g is the gravitational acceleration (9.8 m/s^2).

h = (121.5 kJ) / (51 kg * 9.8 m/s^2)

Calculating that out, we get:

h ≈ 0.24 meters

So, based on their milk intake, this person can climb approximately 0.24 meters. Not quite a mountain, but hey, every little hill counts, right?

Answer 2

To find out how high the person can climb based on the energy intake from the milk, we need to calculate the total energy obtained from the milk and then determine the height that can be achieved using this energy.

Step 1: Calculate the total energy obtained from the milk
The person drinks 270 g of milk, and the caloric value of milk is approximately 3.0 kJ/g. So, the total energy obtained from the milk is:
270 g * 3.0 kJ/g = 810 kJ

Step 2: Calculate the work done in ascending
Since only 15% of the energy is converted to mechanical work, we need to calculate 15% of the total energy obtained from the milk. The work done in ascending is given by the formula mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Using the formula mgh = 0.15 * Total Energy, we can solve for h:

0.15 * Total Energy = mgh
h = (0.15 * Total Energy) / (mg)

Step 3: Plug in the values and calculate the height
The given mass of the person is 51 kg, and the acceleration due to gravity is 9.8 m/s^2.

h = (0.15 * 810 kJ) / (51 kg * 9.8 m/s^2)
h = (0.15 * 810000 J) / (499.8 N)
h ≈ 24.392 m

Therefore, based on the energy intake from the milk, the person can climb approximately 24.392 meters.

Answer 3

To solve this problem, we need to follow these steps:

Step 1: Convert the given mass of milk into energy.
We are given that the person drinks 270 g of milk, and the milk has a "caloric" value of 3.0 kJ/g. To calculate the energy, we can multiply the mass of milk by the caloric value.
Energy = Mass * Caloric Value
Energy = 270 g * 3.0 kJ/g

Step 2: Convert the energy into mechanical work.
Since only 15% of the energy in milk is converted to mechanical work, we need to calculate 15% of the energy obtained in the previous step.
Mechanical Work = Energy * 0.15

Step 3: Calculate the height the person can climb using the mechanical work.
The work done in ascending is given by mgh, where m is the mass, g is the gravitational acceleration, and h is the height.
We have already calculated the mechanical work, and we are given the mass of the person (51 kg) and the gravitational acceleration (9.8 m/s^2). Now we can rearrange the formula to solve for h:
h = Mechanical Work / (mass * g)

Let's plug in the values and solve the equation:

Step 1: Convert the given mass of milk into energy.
Energy = 270 g * 3.0 kJ/g
Energy = 810 kJ

Step 2: Convert the energy into mechanical work.
Mechanical Work = 810 kJ * 0.15
Mechanical Work = 121.5 kJ

Step 3: Calculate the height the person can climb using the mechanical work.
h = Mechanical Work / (mass * g)
h = 121.5 kJ / (51 kg * 9.8 m/s^2)
h = 121.5 kJ / 499.8 N (Note: we're using N/kg for the gravitational acceleration, which is the same as m/s^2)

Simplifying the equation, we find:
h ≈ 0.244 m

Therefore, based on the energy intake, the person can climb approximately 0.244 meters.