Question

A chocolate bar gives a 72kg mountaineer 2.2mj of energy. If he were able to put this entirely into a store of his GPE, how tall a mountain could he climb?

Answer 1

Using the gravitational potential energy formula, a 72kg mountaineer who consumes 2.2 MJ from a chocolate bar could theoretically climb a mountain approximately 3118 meters tall, assuming all the energy is converted into GPE.

Step-by-step explanation:

To find out how tall a mountain a 72kg mountaineer could climb using 2.2 MJ (mega-joules) of energy gained from a chocolate bar, we use the formula for gravitational potential energy (GPE), which is GPE = mgh, where m is mass in kilograms, g is the acceleration due to gravity (9.8 m/s2 on Earth), and h is height in meters.

Solving for height h, we have h = GPE / (mg).

Using the mountaineer's mass and the energy provided by the chocolate bar:

• Convert 2.2 MJ to joules:
  2.2 MJ = 2,200,000 J
• Calculate the maximum height (h):
  h = 2,200,000 J / (72 kg × 9.8 m/s2)
• Perform the calculation:
  h ≈ 2,200,000 J / (705.6 kg·m/s2)
• Final result:h ≈ 3118 meters

The mountaineer could theoretically climb a mountain approximately 3118 meters tall if all the energy from the chocolate bar were converted into gravitational potential energy.