Human Performance

In this lab, you will explore the performance of the human body (your own). In particular, you will look at power and jumping distance - of course you are welcome to explore other aspects as you think of them.

Power
Power is the amount of work done in a given period of time. The power of a particular object (or person) is:
screenshot_01 (if work is in Joules and time is in seconds, this would mean power is in Joules/second - we call this a Watt).
So, to calculate the power of a human you simply need to find out how much work you do and how long it takes. Consider lifting a 1 kg mass 1 meter at a constant speed. You would have to push on this upward with 9.8 Newtons. Work can be calculated as:
screenshot_02 where θ is the angle between the force and the direction of the displacement (in this case that would be either 0 degrees or 0 radians). Thus, the work done would be:
screenshot_04
Now, suppose that this motion took 2 seconds, then the power would be:
screenshot_05 You can see that if this motion took 10 seconds, the power would be much less (but the work would be the same).
(you might be interested in converting this to units of HorsePower, 1horsepower = 746 Watts). You might also be interested in different units for work and energy. 1 calorie is 4.18 Joules (but this is not a food calorie - 1 food Calorie = 1000 calories I don't know why) - apparently, according to wikipedia, the food calorie has a capitol C (1 Calorie = 1000 calorie).

What if you did not move it at constant speed? According to the work energy theorem, it does not matter.
Here is one version:
screenshot_06 So as long as it starts and stops at the same speed (most likely 0 m/s), the change in kinetic energy will be zero.

What about running up a flight of stairs? How would the power of a person compare in these cases? Try it.
Can you think of any other situations to measure power?

Jumping
If you jump up, how much work do you do? How high do you jump? What is average force you exert on the floor while jumping?

1. Determine your mass - 1 kg = 2.2 pounds.
2. Get ready to jump. Measure the location of your center of mass while in the crouching position (call this y1) Your center of mass is typically just above your waist.
3. Measure the location of your center of mass while standing (this will be the position right when you leave the ground). Call this y2.
4. Jump. Have someone measure the location of your center of mass at the highest point. Call this y3.

Analysis
1. First consider the motion going from crouch to the highest point of the jump. What is the Work done on the person? What is the change in gravitational potential? What is the change in kinetic energy? What is the change in internal energy of the jumper?
2. Now consider the position just as the jumper leaves the ground to the position at the highest point. Using the work-energy theorem, find the velocity just as the jumper leaves the ground.
3. Now consider the crouch to standing position. Use the above to find the average force exerted by the floor on the person.
4. Now consider the momentum principle during jumping. If the force is constant, how long are you in contact with the floor during the jump?

You can check your answer by using the jump plate. (I will show you in lab)