lol, ok I lied, I suck at math, and it has been over 5 years since I worked an equation like that. Well I did get an A+ all year in Geometry, but that is because I was in to 3D stuff at the time and I paid a lot of attention in that class.caribe wrote:TryRedpoint wrote:I don't get it, what did that sentence have anything to do with me appearing to be young, was it the paint part? O did you think I meant finger paint lol
I/mg = 1 + SQRT(1 + 2fM/mg)
Which brand of rope do you prefer?
Subtract the two definite integrals from the runner integral and then divide by the time interval for the average friction in the interval.caribe wrote:The integral of the runner's force/time curve with respect to time minus analogous integrals of the belayer and the climber curves should quantify the force lost due to friction in the system throughout the duration of the fall.
_____ BTW: I know that in a friction-free world the rope would just flow apart. The individual fibers are not as long as the whole; it is friction keeping the rope together.
Yes if not for the force being taken up by the rope, the slope (gain in force on the runner over time) of the blue curve would be steeper.ynot wrote:I can't get my brain around all the math, anymore. But the graph makes it painfully obvious that solid pro is essential. Doesn't the curve show rope stretch?
_____ Think of the difference in the force imparted over time between being tackled by the Michelin Man compared to Iron Man. The maximum impulse force during the collision with Iron man is greater because Iron man is harder--less deformable. You therefore have a harder time getting out of bed tomorrow after being creamed by Iron man.
_____ Falling on a static rope would produce a much higher blue line sooner than falling on a dynamic rope because there is less stretch in the static line.
_____ The data if graphed in terms of force on the Y axis and displacement (stretch) on the X axis would get to the elastic modulus (rope stretch) more directly. Stuff that is stiffer takes a large force to deform a little. change in Y divided by change in X = slope. Big change in Y divided by small change in X gives you a big slope, high elastic modulus, stiffer material. To cause deformation in material takes time so time on the X axis (in the graph under consideration) is directly proportional to displacement.