OK it’s time to get a bit serious, don’t worry, it won’t hurt. Most figures are just rounded for illustration, stick your own numbers in place.

**100 step ups** with right leg the 100 with left . Step height 0.18m (18cm). My mass 60kg? Take g (gravitational field strength) as 10 N/kg

- Work done by the body equals gravitational potential energy gained, and only when going up. The Earth’s gravity does the work on the way down.
- Gain in gravitation potential energy (for each step) = mass x g x height change = 60 x 10 x 0.18 = 108 joule
- 200 steps performed, so total work done = 200 x 108 = 21,600 joule
- Total time taken = 200 seconds
- Power = work done ÷ time = 21,600 ÷ 200 = 108 watts so keep going to light the house.

**100 sit ups**

Same theory and equation, just what is the height change and mass lifted? You are only lifting the body above your sitting backside, and the ‘centre of mass’ is just over halfway up the torso, about the bottom of your ribs. This is about 40cm (0.4m). 80% of body mass is above the legs, so I am lifting 48kg

- Gain in gravitation potential energy (for each sit-up) = mass x g x height change = 48 x 10 x 0.4 = 192 joule
- with 100 sit-ups performed total work done = 192 x 100 = 19,200 joule

**35 push-ups**

Same theory and equation again, but what is height change (all the mass is being lifted.) The centre of mass of the whole body is the cross. When doing push ups this will rise about 35cm (0.35m).

- Gain in gravitation potential energy (for each push-up) = mass x g x height change = 60 x 10 x 0.35 = 210 joule
- with 35 push-ups performed total work done = 192 x 35 = 7350 joule

**100 ab crunches**

Same theory and equation again, centre of mass position is nearer the shoulders than for sit-ups and less of the body is actually lifted. Guessing at 50% of mass lifted, a distance of 10 cm (0.1m)

- Gain in gravitation potential energy (for each crunch) = mass x g x height change = 30 x 10 x 0.1 = 30 joule
- with 10 crunches performed total work done = 30 x 10= 300 joule

**Plank 3 minutes**

Well, no calculations can be done. Just holding the body still, without raising it, doesn’t do any work. Certainly chemical energy is being used and muscles stressed, but nothing can be calculated, you’ll just have to be satisfied with it doing you good.

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I like this. Since it’s been over 25 years since my last physics class I won’t add any equations, but I have a couple comments.

– For push ups – I don’t believe you are really pushing up your entire mass since you are resting on your hands and feet. I’m sure there is some center of balance below which the weight doesn’t count.

– For the plank – while your body is not lifting in great movements, I believe there is some oscillation where your gravity is pulling down and your core muscles are pulling back to keep you aligned. I have no idea what the formula would be, but some Physics PhD should be able to whip something up.

Cheers

Once a physics teacher, always a physics teacher?