How much energy in kilocalories is expended against gravity alone by a 75- kg man climbing 1500 m up a mountain?
(75 kg) (1500m) (9.8 m/sec2) / 4184 J = 263 kcals
Calculate the gravitational potential energy of the water in a lake of volume 100km^3 (mass=1.0x10^14kg). The lake has an average height of 50m above the hydroelectric generators at the base of the dam holding the water back.
Well, let me calculate that for you. Take a seat and prepare for some mathematical acrobatics!
First things first, we need to find out the potential energy the man gains by climbing up the mountain. The formula for potential energy is mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
So, the potential energy gained by the man is (75 kg)(9.8 m/s^2)(1500 m) = 1,102,500 J.
Now, let's convert that into kilocalories. One kilocalorie is equal to approximately 4184 Joules.
Therefore, the energy expended against gravity alone is 1,102,500 J / 4184 J/kcal = 263.56 kilocalories.
Now, that's quite a lot of energy! I hope the man had a good snack before the climb.
To calculate the energy expended against gravity alone, we can use the formula:
Energy (in kilocalories) = weight × distance × gravitational acceleration
First, let's convert the weight from kilograms to Newtons using the formula: weight (in Newtons) = mass (in kilograms) × gravitational acceleration.
Given:
Mass of the man (m) = 75 kg
Gravitational acceleration (g) = 9.8 m/s^2
Distance (d) = 1500 m
Weight (in Newtons) = 75 kg × 9.8 m/s^2
Weight = 735 Newtons
Now we can calculate the energy:
Energy (in kilocalories) = 735 N × 1500 m × (1 kcal/4186 J)
Using the conversion factor of 1 kilocalorie (kcal) = 4186 joules (J)
Energy (in kilocalories) ≈ 27.8 kcal
Therefore, a 75-kg man climbing 1500 m up a mountain expends approximately 27.8 kilocalories against gravity alone.
To calculate the energy expended against gravity alone by a 75 kg man climbing 1500 m up a mountain, we need to use the formula:
Energy = force × distance
The force can be calculated using the formula:
Force = weight × gravity
Where weight is the mass of the man × acceleration due to gravity, and gravity is approximately 9.8 m/s².
First, calculate the weight of the man:
Weight = mass × gravity
Weight = 75 kg × 9.8 m/s²
Weight = 735 N (Newton)
Now, calculate the energy:
Energy = force × distance
Energy = weight × distance
Energy = 735 N × 1500 m
To convert the result to kilocalories, we need to know the conversion factor between Joules and kilocalories. 1 kilocalorie is approximately equal to 4.184 kilojoules, or 1 kilocalorie = 4184 J.
Therefore:
Energy in kilocalories = (735 N × 1500 m) / (4184 J/kcal)
Calculating this value gives us the final result of the amount of energy expended against gravity alone by the man climbing:
Energy in kilocalories ≈ (735 N × 1500 m) / (4184 J/kcal)
Please note that this is a rough approximation as it assumes that the entire energy expenditure while climbing is due to gravity alone, without considering other factors such as friction or metabolic efficiency.