You eat a 200-Calorie (200,000 cal) lean hamburger for lunch. Given that 1 cal = 4.2 J, you decide to burn it off by running up stairs in a tall building.

Assume:
- You weigh 145 lbs (approximately 65 kg or 640 Newtons).
- Each flight of stairs has a vertical distance of 8 meters.

If the energy burned is equal to the work done against gravity (\(mgh\)), approximately how many stories do you need to climb to completely "burn off" the hamburger?

To burn off a 200 Cal hamburger, you need to climb approximately 164 stories assuming the energy burned is equivalent to the work done against gravity. The calculation involves converting Calories to joules, then using the gravitational potential energy formula with given weight and height values.

To determine how many stories you need to climb to burn off a 200 Cal hamburger, we follow these steps:

First, convert the energy from Calories to joules:

200 Cal = 200,000 cal (since 1 Cal = 1000 cal)

200,000 cal x 4.2 J/cal = 840,000 J

Next, calculate the work done for climbing using the gravitational potential energy formula (mgh):

W = mgh

The weight (m) is 640 Newtons, the height (h) for each story is 8 meters, and g (acceleration due to gravity) is 9.8 m/s².

Let the number of stories be n.

Thus, Work done = 640 N x 8 m x n = 5120 n J

Set the energy burned equal to the work done to find n:

840,000 J = 5120 n J

n ≈ 164

Therefore, you need to climb approximately 164 stories to completely burn off that 200 Cal hamburger.