The most basic and important piece of gear to safely climb is a rope. When someone is climbing hundreds of feet off the ground they have a large amount of gravitational potential energy that if they fell, would all be transferred into kinetic energy before they hit the ground. Thankfully this is not always the case. The best ropes for climbing are called "dynamic climbing ropes" which get their name from their properties. Compared to some ropes a dynamic rope has a lot of stretch in it and can absorb a fall. The elastic properties of these ropes allow the kinetic energy of the fall to be changed into elastic potential energy. The more rope there is in the system the more distance and time there is for this energy to be converted. This reduces the impact of the fall on both the climber and the rope which lowers the injury rates of climbers and the chance a rope will break.
One of the most interesting pieces of rock climbing protection is a piece of hardware called a cam (Grow). This device is placed into a crack in the rock and acts as an anchor for the climber to attach themselves to so that if they fall, they will be stopped from falling to their death.
These cams work due to their special design. They have 4 separate lobes which are joined around a central point. To place a cam the lobes are pulled inwards to decrease the devices overall width, then once inside the crack they are released so that they press outwards against the sides of the crack. What causes this initial outward movements of the lobes is the potential spring energy stored in the springs of the device. However once placed there is still more physics which applies.
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Once the climber is attached to the device by the rope, if they fall, a downwards force will act upon the cam. This downward force, due to the torque caused by the lobes rotating around their center, translates into a force outwards which in turn secures the cam more tightly in the rock and hopefully stops the climber who has fallen before they hit the ground.