A piece of chocolate cake contains about 400 Calories (food). How many 8-inch steps (expressed to 2 significant figures) must a 180-lb man climb to expend the 400 Cal from the piece of cake?

P.E. = mgh; m = mass; g = acceleration due to gravity 9.8 m/s2; h = height.

(Hint – remember the derived units for a joule.)

Update:

I got 10. but for some reason it's wrong. I'm not sure why. I tried putting "10." "10" "1E1" "1 E 1" but none of it was right.

Update 2:

correction to the last two inputs "1.0E1" "1.0 E 1"

Relevance
• 8 years ago

First off I would convert calories into joules (1 Calorie = 4.18 Joules)

400*4.18 = 1672J

Then I would convert inches into meters (1 inch = 0.0254 meter)

8*0.0254 = 0.2032m

Then I would convert pounds into kilograms (1 pound = 0.453592 kilogram)

Then you set up the equation

Amount of Energy from the cake = PE = mgh

1672 = 81.6466*9.81*0.2032*x (x = amount of 8-inch steps)

Solve for x...and you get 10.273 ---sig figs--->10. steps. It's important that the "." is there since 10 has only 1 sig fig, and since 10.0 has 3 sig figs.

Source(s): I was an AP Physics B student
• 8 years ago

This is a great example of why the metric system is way better especially for science stuff

a regular calorie of energy = 4.184 J

BUT a calorie isn't always just a calorie ... like when it comes to chocolate cake (or any food )

a single food calorie is actually 1000 regular calories ... so your answer is 1/1000 of the actual answer:

so 400 food calories = 400 x 1000 x 4.184 = 1673600 J

so 1673600 = mgh

1673600 = 180 lb x [1 kg / 2.2 lb] x 9.8 h

h = (1673600 x 2.2) / (180 x 9.8)

h = 2087 m

Now 8 in = 8 in x [2.54 cm / in] x [1 m / 100 cm] = 0.2032 m

Number of steps = 2087 / 0.2032

Number of steps = 10271 = 10000 (to 1 sig fig) ... [b/c the least number of sig figs in the given data is 1]