Chocolate vs Weight Lifting

Classical Mechanics Level 2

You eat a 100 grams chocolate bar which provides you with $2300 \text{kJ}$ of energy. In the fear of getting fat, you want to do a workout that will burn this energy you just ate.

You see 2 packs of water bottles. Each pack has 6 filled bottles of each 1.5 L. How many times do you have to lift these packs to a height of 1 meter to at least burn all the energy of the chocolate you have just eaten?

Detail and Assumptions:

While repeating you can ignore the energy needed to place the bottles back on the ground. (Imagine dropping them.)
The density of water is 1 kilogram per liter.
You are on a place on the earth where gravity accelerates all objects downwards at 10 meters per second squared.
You can ignore all biological processes. Only focus on the lifting.
You lift the both the packs at a right angle to the ground.
You can ignore the mass of packaging of the bottles.

Bonus: If lifting the six-packs takes you 2 seconds and dropping the six-packs takes 1 seconds (including you moving your hands downwards to grab the bottles again, which can be ignored in terms of energy). How long would it take you to burn all the calories of the chocolate you ate?

Formula: $E=mgh$

E is the gravitational potential energy.
g is the gravitational acceleration
h is the change in an object's distance to the center of mass (how high the bottles are lifted)

Fun Side Note: Will you eat chocolate today?

The answer is 12778.

1 solution

Callum M
Feb 23, 2018

Since each liter of water is 1kg, so a 1.5L bottle of water is 1.5kg. We have six bottles per pack so we have $1.5kg \times 6 = 9kg$ per pack. We have two packs so altogether we have 18kg to lift.

Using our Energy formula E = mgh we can plug in 18 for m, 10 for g, and 1 for h (since we want to lift them to a height of 1m). We get $E = 18 \times 10 \times 1$ so E = 108J . This is how much energy we will burn for every lift.

Kilo means 1000 so 2300kJ means we have 2,300,000J of energy for the chocolate bar. we can divide the amount to burn by the amount we burn, which is $\frac{2,300,000}{180}$

This gives us 12,777 $\frac{7}{9}$ lifts, but we must round up since we have to do a full lift and we arrive at 12,778 lifts to burn all that energy.

Bonus: If it takes 2 seconds to lift up, and 1 second to drop, it should take us a total of 3 seconds to do a full lift. So each lift takes us 3 seconds, we do this 12,778 times $12,778 \times 3$ gives us about 38,333 total seconds, which is approximately 10 $\frac{1}{2}$ hours.

Chocolate vs Weight Lifting

The answer is 12778.

1 solution

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