Final answer:
The question addresses finding load intensities for equilibrium under different loading scenarios on a foundation in the field of physics, specifically statics. It involves applying concepts of equilibrium and mechanics of materials to determine the varying load distributions represented by w1 and w2.
Step-by-step explanation:
The student's question involves finding load intensities for equilibrium under different loading conditions on a foundation, which is rooted in statics, a branch of physics specifically concerned with analysis of forces on physical systems in a state of balance. In statics, one applies the concept of equilibrium, where the sum of forces and the sum of moments about any point equals zero. When dealing with linearly varying loads, one needs to establish equations based on equilibrium conditions - the sum of the vertical forces must equate to zero for the system to be in static equilibrium.
In the given scenario, the load distribution on the bottom of the foundation is assumed to be linearly varying. Let's analyze each case:
When the load is concentrated at the center, the load intensities, w1 and w2, will be equal.
When the load is uniformly distributed across the entire foundation, the load intensity, w1 and w2, will be equal.
When the load is applied at one end of the foundation, the load intensity, w1, will be greater than w2.
When the load is applied at both ends of the foundation, the load intensity, w1 and w2, will be equal.
For a concentrated load at the center of the foundation, the varying load distribution would be symmetrical, with w1 and w2 being equal and their resultant passing through the center. A uniformly distributed load would result in constant w1 and w2 across the entire length of the foundation. If the load is applied at one end, w1 or w2 would be larger at the loaded end. Lastly, if the load is applied at both ends of the foundation, the intensities w1 and w2 would be higher at the ends with a lower intensity in the middle. To determine the actual values of w1 and w2 for each case, one would set up equations from the principles of mechanics of materials and solve for the unknowns.