In a mountain-climbing technique called the Tyroleantraverse, a rope is anchored on both ends (to rocks or strongtrees) across a deep chasm, and then a climber traverses therope while attached by a sling as in Fig. 12-102. This techniquegenerates tremendous forces in the rope and anchors,so a basic understanding of physics is crucial for safety. Atypical climbing rope can undergo a tension force of perhaps29 kN before breaking, and a safety factor of 10 is usuallyrecommended. The length of rope used in the Tyroleantraverse must allow for some sag to remain in the recommendedsafety range. Consider a 75-kg climber at the centerof a Tyrolean traverse, spanning a 25-m chasm, (a) To bewithin its recommended safety range, what minimumdistance x must the rope sag? (b) If the Tyrolean traverse isset up incorrectly so that the rope sags by only one-fourththe distancefound in (a),determine thetension in therope. Will therope break?FIGURE 12-102 96.

Lectures 1 2 and 3 Average Speed & Average Velocity vavgdistancetime=dt *speed is a scalar (magnitude with no direction vavgdisplacementtime= rt * velocity is a vector (has direction) → UNITS: ms vavg and r point in direction of motion vx= xf-x0t → xf=x0+t(vx) *with constant velocity Negative slope = negative velocity Steeper slope = faster speed Acceleration aavgvt *rate of change of velocity (slowing, speeding, changing direction) aavgv - n+1 n → UNITS: ms 2 → If v and a are point in the same direction, the object is speeding up afree fall0 ms2 → 1 dimensional acceleration down a slope: as= g(sin) Ki