Lab 10: Work

I'm all for practical learning, but physics in itself feels like an exercise in reinventing the wheel--over and over and over again. Everything we prove is something that has mathematically modeled hundreds of years ago. That's why I aspire to be an engineer instead of a physicist--to create something of practical use to people who don't live inside an underground Switzerland lab. And honestly, we're too busy trying to jump through a bunch of hoops within a predefined time limit during a lab to actually sit down and think about all the relationships and why they are--much easier to see the symbolic relations without distractions like how to enter a constant in a proprietary software called Logger Pro.

But this lab isn't just work, it's about work. More specifically, it's about defining work in a physical context, and how physics work coincides with the common understanding of work. We measure work in three ways: walking up stairs, running up stairs, and pulling a weighted backpack up a distance with slippery rope. Since the physics definition of work is just:

Work = Force * Distance

... if we know the carrying weight and the displacement, then there should be no problem in calculating it. The hardest part is actually doing the experiment.

First we measured the vertical height of each step to be 17 cm, with a total of 26 steps, for a total height of 442 cm. The first task, then, is to walk up the stairs in an arbitrary pace. As with all labs before, we use the small plastic timer, which does it's job. What it doesn't capture is the precise time or place in which the stairs start or finish, as this requires a manual button-push, introducing human error. For the run--self-explanatory!

	Time (s)
Walk	16.08
Run	4.96
Rope	27.82

Next, we use a rope and pulley system tied to a balcony at the top of the stairs (same height) to lift backpacks weighted 9 kg.

If the incline of the stairs is 30º, then it should only take half the force to traverse it compared to climbing vertically.

Note that these are not the stairs we climbed, this is for illustration purposes only!

F = mg sin30°

However, note that the distance is doubled. Therefore, since work is force times distance, there should be no change in work over different angles:

(1/2)F * 2h = F * h

The difference then, comes down to mass. Climbing stairs is equivalent to carrying the entire body weight, which is much heavier than pulling up a 9 kg backpack. The work required for each activity (assuming 160lbs body weight, or roughly 72.6 kg) is:

 

	Mass (kg)	Force (N)	Distance (m)	Work (J)
Walk	72.6	711.48	8.84	6289
Run	72.6	711.48	8.84	6289
Rope	9	88.20	4.42	390

Therefore, while lifting things target a specific muscle for working out, running would be preferred for burning calories. Speaking of calories, apparently a calorie is defined as "the amount of energy required to warm 1 g of air-free water from 14.5 °C to 15.5 °C at a constant pressure of 101.325 kPa (1 atm)". The definition requires the ambient temperature to be at 15 °C, so given that assumption (the day was much hotter!), the conversion is approximately 0.2389 calories per joule of energy. We could also figure power using the formula:

Power = Work / Time

The results are:

	Work (J)	Time (s)	Calories	Power (w)	kcal
Walk	6289	26.08	1502.46	241.14	1.50
Run	6289	4.96	1502.46	1267.94	1.50
Rope	390	27.82	93.17	14.02	0.09

The last column is kilo-calories, which is commonly referred to as a "calorie" in nutrition, so one would need to burn 1000 actual calories in order to burn what is commonly referred to as a calorie. Considering that climbing these stairs only burnt 1.5 kcal, a person would need to climb the stairs roughly 634 more times in order to burn off the 952-calorie Kentucky Club Salad from the WOW Cafe. Wow. Looks like I need to stop ordering 1180-calorie Texas Toast Burgers.