Final answer:
In the scenario provided, to determine the forces on the ladder placed against the house, one must apply the principles of static equilibrium. These include summing moments to zero about any point and ensuring that the sum of vertical and horizontal forces is also zero. Portable ladders must withstand at least four times their maximum intended load.
Step-by-step explanation:
Analysis of Forces on a Ladder
Considering the scenario where a 70.0 kg person places a 6.00-m aluminum ladder against a house, with the base 2.00 m from the house, we can analyze the forces at work. Since the ladder is in static equilibrium, the principle of moments tells us that the sum of clockwise moments about any point is equal to the sum of anticlockwise moments about that same point. Knowing the masses of the person and the ladder allows us to calculate the forces due to gravity acting on them. The ladder itself acts as a uniform, rigid body in static equilibrium, and the forces on the ladder at the top and bottom can be determined by setting up equations for the torques and forces in the vertical and horizontal directions.
For the ladder to be in equilibrium, the forces acting on it must satisfy the conditions for equilibrium: the sum of vertical forces must be zero, the sum of horizontal forces must be zero, and the sum of moments about any point must also be zero. Because the ladder rests against a frictionless surface, there would be a normal force at the top acting towards the wall and a normal force at the bottom acting away from the wall. The person's weight adds an additional force further away from the pivot point at the bottom compared to the ladder's own weight.
To find the magnitudes of the normal forces at the base and the force at the top, we would set up equations based on the conditions of static equilibrium (sum of forces in any direction equals zero, sum of moments about any point equals zero) and solve for the unknowns. This involves calculating the moments due to the person standing 3 m from the bottom, the ladder's center of mass that is 2 m from the bottom, and the lack of friction at the top end. We do not provide the calculations here, as they are not the focus of the explanation; however, the strategy involves using the above mentioned principles and solving the resulting system of equations.
As for the question posed by the student regarding portable ladders, according to most safety standards, a portable ladder must be able to withstand at least four times its maximum intended load, except that each rung on ladders shall be capable of supporting a single concentrated load of at least 250 pounds applied in the middle of the rung. Hence, the correct answer would be option 3) 4 times the maximum load.