Final answer:
To find the normal and friction forces at the ladder's base, apply static equilibrium principles, balancing forces and torques around a pivot point, usually the base.
Step-by-step explanation:
In this scenario, with a ladder resting against a frictionless surface, we can use the principles of static equilibrium to determine the reaction forces. With a person of mass 70.0 kg standing 3.00 m from the bottom of a 6.00-m long ladder, and the center of mass of the ladder (10.0 kg) 2.00 m from the bottom, the forces and moments need to be balanced around a pivot point, typically at the base.
The ladder's weight and the person's weight create a moment (torque) about the pivot point. The normal force reacts vertically upwards, and the friction force acts horizontally against the tendency to slip. By setting up equations for the moments to be balanced and the horizontal and vertical forces to be equal and opposite, we solve for the normal reaction and static friction forces. As the ladder's weight and angle remain constant, the coefficient of friction required to prevent slipping can also be calculated (not provided in the question but can be inferred).
The significance of the static equilibrium in these problems is that the results remain valid regardless of the ladder's length; what matters are the weights and angles involved. The balance of torques and forces ensures that the ladder remains stationary and does not slip.