Re: why does your hands burn when you slide down a rope really fast?

It's because of the transformation of your kinetic energy (the energy of motion) to heat, which is the energy of motion (kinetic energy) of the molecules in your hands and the rope. As you slide down the rope, the molecules of your hands and the molecules of the rope collide with each other, the result being what we call friction. The mechanical work done by your hands' molecules on the rope's molecules slows you, but makes the interface between your hands and the rope hot. The molecules of your hands and the rope are essentially knocked into motion (vibration) as they collide with each other, and the increased motion is what we call "more heat".

From a purely conservation-of-energy viewpoint it is possible to calculate how much "heat" your hands and rope make. Let's assume that you are grabbing the rope just hard enough to keep your descent speed constant at about 1 meter per second. I have a feeling that that's pretty fast for a rope, but let's use it for discussion purposes. The power being put into a system like this one is equal to the force times the velocity (you can work out the dimensions of force times velocity and verify for yourself that you obtain the dimensions of power). If your mass is 60 kg then your weight is 60 x 9.8 (where 9.8 meters per second per second is the gravitational acceleration at the surface of the earth) 588 Newtons. 588 Newtons times 1 meter per second is 588 Watts.

Let's calculate the power another way. In my hypothetical scenario you are obtaining one meter's worth of gravitational energy every second. The work done by gravity is equal to the mass of the object times the height change times the gravitational constant, or
W = m g h.
Since your mass is 60 kilograms (in this problem!) the work done in every second is 60 x 9.8 x 1 or 588 Joules. Since that is in one second the power is 588 Watts (a Watt is just one Joule per second). You can see that both ways of calculating the power arrive at the same answer!

Okay, you can look in almost any physics textbook and discover that the "Joule equivalent of heat" is about 4.2 Joules/cal. That means that for every 4.2 Joules of work you do on a system it obtains one calorie of heat energy. In the hypothetical problem we are obtaining 588 Watts, or 588 Joules per second. Using the conversion factor gives us
588 / 4.2 = 140 calories per second.

One calorie is the amount of heat needed to raise one gram of water by 1 Celcius (or Kelvin) degree of temperature. That's only an approximation which holds strictly when the water starts at 15 degrees C, but it's close enough. So if you had one gram of water you could heat it 140 Celcius degrees in one second (assuming you could somehow get all the gravitational heat energy from the hand/rope interface to the water!!), or 140 grams of water up one degree Celcius in one second, etc. Since your body is made up of mostly water let's make the simplifying assumption that 140 grams of your hands would be heated about one Celcius degree in one second, or 14 grams up 10 degrees, or 1.4 grams up 100 degrees (you get the idea?). This neglects the energy that would go into the rope, but we're just looking for an approximation.

Now, I would say that that's quite a bit of heat!! If you slid on the rope for ten seconds your hands and the rope would have to absorb 1,400 calories of heat, and that's a lot. Perhaps you can see now why your hands get hot when you slide down the rope!

John Link, MadSci Physicist