Final answer:
Using principles of static equilibrium, the forces on the ladder at the top and bottom can be calculated. The normal force at the base supports the combined weight of the person and ladder, and the force at the top is due to the wall's contact.
Step-by-step explanation:
Calculating Forces on a Ladder
To determine the magnitudes of the forces on the ladder at the top and the bottom, we should consider the principles of static equilibrium. The ladder, along with the person climbing it, forms a system that must satisfy two conditions: no net force in any direction and no net torque at any point.
First, the normal force at the bottom of the ladder must support the combined weight of the person and the ladder. The weight of the person (Wp) is 70.0 kg × 9.8 m/s², and the weight of the ladder (Wl) is 10.0 kg × 9.8 m/s². The normal force (N) at the base will equal the total weight: N = Wp + Wl.
Second, we must ensure that the ladder is in rotational equilibrium, which means the sum of all torques (τ) about any point is zero. By choosing the base of the ladder as the pivot, we can calculate the torques due to the person and the ladder's center of mass. The force at the top of the ladder can be considered as the force the wall exerts on the ladder, which is perpendicular to the ladder because the wall is assumed frictionless. The condition for rotational equilibrium is: τ due to Wp + τ due to Wl - τ due to Ftop = 0, where Ftop is the force at the top of the ladder.