In one aspect, a clamp for installation onto an elevator car as part of an emergency braking system comprises: a clamp body having an L-shaped profile with a vertical portion for attachment to an elevator car wall of the elevator car and horizontal portion for attachment to an elevator car roof or an elevator car floor of the elevator car; and a pair of opposing brakes disposed on the vertical portion of the clamp body for clamping a mine shaft guide between the brakes for emergency braking. In another aspect, a method of activating an emergency brake of an elevator car comprises: sensing a load of the elevator car; based on the sensed load, dynamically determining a rate at which an emergency brake shall be incrementally engaged; and upon detecting a freefall or overspeed condition of the elevator car, incrementally engaging the emergency brake at the dynamically determined rate.