How Far Can I Hike Up a Mountain After a 500 Calorie Lunch?

[layla2525]

Homework Statement

I am 65 kg and eat a 500 Calorie lunch and go hiking up a mountain afterwards. Assuming that chemical energy is converted to gravitational potential energy with 50% efficiency, approximately how many miles up the mountain can I go before I need my dinner?

0.5 miles

1 mile

2 miles

3 miles

4 miles

Homework Equations

The Attempt at a Solution

I solved for height by (2.0 x 10^(6))/ (65kg)(9.8)
which gave me 301538.4615, and then dived it by 2 because of the efficiency and got 1569.8587, now how can i convert into miles?

 

[layla2525]

250-Calorie* snack, which contains 1x10^6 J

 

[Andre]

250-Calorie* snack, which contains 1x10^6 J

Close yes but 250 calories is not a lot. It's likely that kilo-calories is intended.
What is a relevant equation for potential energy (in units?)

 

[layla2525]

I got 1569 for my efficiency What do I do after I get the Efficiency ?

 

[Nickie]

First, I would like to clarify that the efficiency of converting chemical energy to gravitational potential energy is not always 50%. It can vary depending on the efficiency of the body's metabolism and the type of food consumed.

To convert the height from meters to miles, you can use the conversion factor 1 meter = 0.000621371 miles. This gives a result of approximately 0.98 miles. Therefore, you can go approximately 1 mile up the mountain before needing your dinner.

Another way to approach this problem is by using the formula for gravitational potential energy: PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.

First, we need to calculate the total energy from the lunch, which is 500 Calories or 500,000 calories. Converting this to joules, we get: 500,000 x 4.184 = 2,092,000 J.

Since the efficiency is 50%, we can calculate the gravitational potential energy as: PE = 0.5 x 2,092,000 J = 1,046,000 J.

Using the same formula as before, we can solve for h: h = PE/(mg) = 1,046,000 J / (65kg x 9.8 m/s^2) = 1,591.42 m.

Converting this to miles, we get approximately 0.99 miles. This is consistent with our previous calculation.

Therefore, you can go approximately 1 mile up the mountain before needing your dinner. Keep in mind that this is an estimate and may vary depending on individual factors.