Re: How many calories (kCal) are burned doing arm curls?

Hi Munro,

Your manipulation of the equation is correct, but your use of acceleration is incorrect. This will be immediately apparent if you consider that when you start to push the weight up, your arm initially is at rest. When you finish, your arm is also at rest. Thus, your arm has gone from 0 ms^-1 to 0 ms^-1. There is no net change in speed and average acceleration is zero.

When I was in my first year of high school, my physics teacher started to teach about motion. Seeing that I was talking and not listening, she blurted out "Kingsley, what is Newton's first law of motion?". To her surprise I recited the law word for word from a book I had read the night before. However, not to let one of her students get the upper hand, she then asked what type of force I meant. I was stumped because that wasn't in the book! She had succeeded in puzzling me and I started paying attention.

The answer she was looking for was resultant force, the sum of all the forces acting in the system.

In this system there are three forces: the force of your arm muscles, air resistance and the force due to gravity. You can ignore air resistance because this force is small. You can also ignore the force from your arm because the net acceleration is zero.

(F=ma - zero accelation gives zero force)

It is often assumed that using a figure in kg will give a give a figure in kJ when using the equation w=mad. However, the joule is the unit of work. The kilogram is the unit of mass and 1J of work is done when 1 Kg is accelerated at 1ms^-2 over a distance of 1 m in the direction of the force.

This figure may also seem high to you due to the confusing units of "calorie" and "Calorie". Food companies and nutritionists might say that your typical dietary intake is 1800 Calories whereas a biologist might say that it is 1800 Kcal. Note the use of upper and lower case 'C'. 1 Calorie = 1000 calories. 26.7 J is equivalent to 6.5 cal or 0.0065 Calories.

I simplified the answer by ignoring sideways motion and dealing only with vertical forces. In this simplified system, sideways motion is irrelevant because work can only be done by moving an object in the direction of the force, i.e. Up or down when dealing with gravity. In reality, a small amount of work is done in moving horizontally because of air resistance.

One more thing to consider. Respiration is only about 40% efficient. The calorie usage was probably nearer to 16.5 calories with the unaccounted 10 calories being converted to heat.

Hope this helps,

Richard Kingsley.