How high can a person (assume a weight of 70 kg) climb on one ounce of chocolate if the heat of combustion (628 kJ) can be converted completely into work associated with vertical displacement?

E = m g h ... h = E / (m g)

h = 628 kJ / (70 kg * 9.81 m/s^2)

1 Joule = 1 kg m/s^2

To determine how high a person can climb on one ounce of chocolate, we need to calculate the potential energy that can be obtained from the heat of combustion of the chocolate and then relate that to the vertical displacement.

1. Convert the mass of chocolate from ounces to kilograms:
1 ounce = 28.35 grams
1 kilogram = 1000 grams
Therefore, 1 ounce = 28.35 / 1000 = 0.02835 kg

2. Calculate the potential energy (PE) obtained from the heat of combustion of the chocolate using the formula:
PE = energy / mass
PE = 628 kJ / 0.02835 kg
PE = 22161.57 kJ/kg

3. Determine the gravitational potential energy (GPE) associated with vertical displacement:
GPE = mass x gravity x height
GPE = 70 kg x 9.8 m/s² x height

4. Equate the potential energy from the combustion of the chocolate to the gravitational potential energy associated with the vertical displacement:
22161.57 kJ/kg = 70 kg x 9.8 m/s² x height

5. Solve for the height:
height = 22161.57 kJ/kg / (70 kg x 9.8 m/s²)
height = 31.79 meters

Therefore, a person with a weight of 70 kg can climb approximately 31.79 meters on one ounce of chocolate if the heat of combustion is completely converted into work associated with vertical displacement.

To determine how high a person can climb on one ounce of chocolate, we need to calculate the energy content of the chocolate and then convert it into potential energy associated with vertical displacement.

Step 1: Convert the weight of the chocolate from ounces to kilograms.
Since 1 ounce is approximately equal to 28.35 grams, we have:
1 ounce ≈ 0.02835 kg.

Step 2: Calculate the energy content of the chocolate in joules.
Given the heat of combustion is 628 kJ (kilojoules), we convert it to joules:
628 kJ × 1000 = 628,000 J.

Step 3: Calculate the potential energy associated with the vertical displacement.
The potential energy can be calculated using the formula:
Potential Energy (PE) = mass (m) × gravity (g) × height (h).

The person's weight (mass) is 70 kg.
The acceleration due to gravity (g) is approximately 9.8 m/s².

Using the formula, we can express height (h) in terms of potential energy:
PE = mgh,
628,000 J = (70 kg) × (9.8 m/s²) × h.

Solving for h:
h = 628,000 J / (70 kg × 9.8 m/s²).
h ≈ 904.32 meters.

Therefore, a person weighing 70 kg can climb approximately 904.32 meters on one ounce of chocolate if all of its heat of combustion is converted into work associated with vertical displacement.