The label on a candy bar says 470 Calories.Assuming a typical efficiency for energy use by the body, if a 74 kg person were to use the energy in this candy bar to climb stairs, how high could she go?
Exactly what is a "typical efficiency"? Is that a physics term? (Answer:NO)
Labels on candy bars are in food Calories, which is not your obselete physics term "calories". Look up the difference.
Now to answer your question (sort of). Disect it to understand. It assumes 100 percent efficiency
mgh=1000*470* 4.18 check the units.
h= 1000*470*4.18/((74*9.8)) which is plenty high. Now you are at your "typical efficiency" term.
One can "burn" off 470 Calories by about one hour on a stationary bike with moderate effort.
http://www.nutristrategy.com/activitylist.htm
Most of the energy consumed by the body goes to keeping the heart running, and the body warm.
typical efficiency = .25= 25%
To determine how high a 74 kg person could climb using the energy from a candy bar, we will need to calculate the potential energy in the candy bar and then convert it to height.
The energy contained in the candy bar can be calculated using the equation:
Energy = Mass x Gravity x Height
Since we know the mass of the person is 74 kg and the value for gravity is approximately 9.8 m/s^2, we can rewrite the equation as:
Energy = 74 kg x 9.8 m/s^2 x Height
To solve for height, we need to rearrange the equation:
Height = Energy / (Mass x Gravity)
Now let's plug in the known values:
Height = 470 Calories / (74 kg x 9.8 m/s^2)
To proceed further, we need to convert the Calories to joules, as the unit of energy used in the equation is joules.
1 calorie = 4.184 joules
Therefore, 470 Calories = 470 x 4.184 joules.
Height = (470 x 4.184 joules) / (74 kg x 9.8 m/s^2)
Calculating the values:
Height = 1954.88 joules / (725.2 kg·m²/s²)
Height = 2.692 meters
Therefore, a 74 kg person could climb approximately 2.692 meters using the energy from the candy bar.
To calculate how high a person can climb using the energy from a candy bar, we need to consider a few factors. Firstly, we need to determine the amount of potential energy the body can generate from the energy content of the candy bar.
The energy content of the candy bar is given as 470 Calories. However, Calories in this context are actually kilocalories (kcal), which is the unit commonly used in nutrition.
Next, we need to consider the efficiency of energy use by the body. When performing physical activities, the body is not 100% efficient in converting energy into work. Typically, the efficiency is around 20-25%. For our calculation, we'll assume an efficiency of 20%.
Now, let's break down the calculation step by step:
Step 1: Convert Calories to joules
1 Calorie = 4.184 joules
So, the energy content of the candy bar in joules is:
470 Calories * 4.184 joules/Calorie = 1964.68 joules
Step 2: Calculate the potential energy generated
As mentioned earlier, we will assume an efficiency of 20%. To calculate the potential energy generated, we need to multiply the energy content by the efficiency:
Potential Energy = 1964.68 joules * 0.20 = 392.94 joules
Step 3: Calculate the height using potential energy
In the case of climbing stairs, the potential energy gained is converted to gravitational potential energy. The formula for gravitational potential energy is:
Potential Energy (PE) = mass (m) * acceleration due to gravity (g) * height (h)
We can rearrange the formula to solve for height:
h = PE / (m * g)
The mass of the person is given as 74 kg, and the acceleration due to gravity, g, is approximately 9.8 m/s^2.
Plugging in the values:
h = 392.94 joules / (74 kg * 9.8 m/s^2)
h = 392.94 joules / 725.2 kg*m^2/s^2
h ≈ 0.54 meters
Therefore, the person could climb approximately 0.54 meters (or about 1.8 feet) using the energy from the candy bar.