Final answer:
The forces on a ladder can be determined by applying the principles of static equilibrium from physics, which ensure that the sum of the forces and torques is zero. The weight of the person and ladder generates a normal force at the base, and at the frictionless top, a horizontal force is present.
Step-by-step explanation:
When calculating the forces on a ladder in static equilibrium, we apply principles from statics, a branch of mechanics in physics. The conditions require that the sum of the forces and the sum of the moments (torque) around any pivot point must be zero.
For the ladder scenario given, we set the base of the ladder as the pivot to calculate the forces at the top and the bottom. We have the weight of the person (70.0 kg), the weight of the ladder (10.0 kg) acting downwards, and the normal reaction force at the base pushing up. To prevent rotation, the moments around the pivot due to these forces must balance.
We can solve for the forces using the equations for equilibrium:
The sum of vertical forces = 0
The sum of moments about any point = 0
The normal force at the base is equal to the total weight of the ladder and person because it must balance these forces in the vertical direction. The force at the top is due to the interaction between the ladder and the wall, which, if frictionless, only has a horizontal component.