Posted by k on .
Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 1.7 m and then the rope stops her over a distance of 1.0 m.
(a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.)
____ xKaren's weight
(b) In a similar fall, Bill's rope stretches by 25 cm only. How many times his weight will the rope pull on him?
___ x Bill's weight
Which climber is more likely to be hurt?
b) Both are equally subject to injury.
In falling freely 1.7 m, both climbers reach a velocity of sqrt(2g*1.7) = 5.77 m/s and a kinetic energy M g *1.7
The average force needed to stop in a distance is given by
F = KE/X = 1.7Mg/X
That is 1.7/1 = 1.7 times the body weight for Karen and 1.7/0.25 = 6.8 times the body weight of Bill
How would you answer the last question?