The Forces
When building an anchor it is important to consider the forces which will be acting on it. Forces are vector quantities used to measure the interaction between objects. In the case of climbing this is the force the climber will have on the anchor system.Top Roping
When top roping the climber's weight is always below the anchor, so
when the climber falls they are caught by the rope quickly. To
calculate force Newton's Second Law can be applied:
Force= Mass × Acceleration (F=ma);
where
acceleration is the acceleration of gravity (9.81m/s²) and mass is
the mass of the climber (Kg).
Lead Climbing
When taking a lead fall the forces are
much greater because the climber's weight is often above the
anchor. The force is dependent upon the distance of the fall, the
mass of the climber, the time it takes the belayer to stop the climber
and the acceleration due to gravity (9.81 m/s²). Newton's
second law can still be applied but in this case the formula
Force= change in momentum (pfinal-pinitial)/change
in
time
(tfinal-tinital)
By setting inital momentum and inital
time to zero the following equations can be derived:
F=p/t
Momentum is defined as defined as an object's mass times its
velocity (p=mv)
F=mv/t
Velocity can be found by dividing the distance the climber falls by the
time it takes the belayer to stop the fall
F=m(d/t)/t
F= md/t²
Photo:
http://www.chockstone.org/Grampians/Gondwannaland/Falling1l.JPG