A 51 kg person drinks 330. g of milk, which has a "caloric" value of approximately 3.0 kJ/g. If only 18% 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.)]
330 g x 3.0 kJ/g x 0.18 = ?? kJ.
Substitute into mgh for work and solve for h
It says that answer is off by a multiple of ten.
To solve this problem, we need to follow a series of steps:
Step 1: Calculate the total energy intake from the milk consumed.
We know that the person drinks 330g of milk and the caloric value of milk is approximately 3.0 kJ/g. Therefore, the total energy intake can be calculated as follows:
Energy intake = 330g * 3.0 kJ/g
Step 2: Convert the energy intake into joules.
Since the kilojoule (kJ) is a larger unit than the joule (J), we need to convert the energy intake to joules for consistent units. We know that 1 kJ = 1000 J.
Therefore, the total energy intake in joules can be calculated as follows:
Energy intake (J) = Energy intake (kJ) * 1000 J/kJ
Step 3: Determine the amount of energy converted to mechanical work.
We know that only 18% of the energy is converted to mechanical work. Therefore, we can calculate the energy converted to mechanical work as follows:
Energy converted to work (J) = Energy intake (J) * 0.18
Step 4: Calculate the height the person can climb based on the energy converted to work.
The work done in ascending is given by the formula mgh, where m is the mass, g is the gravitational acceleration, and h is the height.
In this case, the mass of the person is given as 51 kg and the gravitational acceleration (g) is 9.8 m/s².
Therefore, the height the person can climb can be calculated as follows:
Height (h) = Energy converted to work (J) / (mass (kg) * g)
Now let's substitute the calculated values into the formula to find the height.
First, let's calculate the total energy intake:
Energy intake = 330g * 3.0 kJ/g
Energy intake = 990 kJ
Next, convert the energy intake to joules:
Energy intake (J) = 990 kJ * 1000 J/kJ
Energy intake (J) = 990,000 J
Now, determine the energy converted to work:
Energy converted to work (J) = 990,000 J * 0.18
Energy converted to work (J) = 178,200 J
Finally, calculate the height:
Height (h) = 178,200 J / (51 kg * 9.8 m/s²)
Height (h) ≈ 352.55 meters
Therefore, based on the given energy intake, the person can climb approximately 352.55 meters.