Study Guide

Forces and Motion Themes

  • Force Diagrams

    Engineering

    Force diagrams are more than required physics material: they’re the backbone of civil and mechanical engineering. Let’s consider one example.

    Imagine building a bridge without analyzing the forces placed upon it, and upon its foundation? Disaster in the making, right there. Forces have to balance out from the top all the way to the bottom, or the whole thing might collapse.

    Here’s a bridge.

    The forces put onto the bridge itself are the forces from the pieces of the bridge itself. Ignoring the force of gravity and normal force as the diagram does, inspect the forces on the pieces of the bridge as a chain reaction of forces from the top on down. See that? The keystone presses outward, as the unmarked gravity pulls it down. The footers and abutments ensure that the pieces on top can’t fall. The top pushes outward, but the bottom pushes inward and the structure stands, supported by balanced forces. The force of gravity and normal forces also balance each other, even though they’re not drawn in here.

    Among other things, civil and mechanical engineers also consider how different placements of forces affect materials. In a bridge, say, or furniture, a building, or vehicle the materials and overall structure need to be strong enough to withstand all of these kinds of force applications, which may occur from people, wind, earthquake, car accident, traffic, etc. Obviously, it depends on the structure, whether bridge, building, vehicle, or something else.

    A compressing situation occurs whenever there’s force from above and below, which causes compression on any kind of material. Some kinds of materials withstand compression better than others. You wouldn’t want to build a skyscraper out of plastic, for example, because it would substantially compress under its own weight. Stainless steel and reinforced concrete do nicely, though.

    Tension occurs whenever there’s an unsupported surface. A ceiling is under tension, a floor not on the ground level, bridge cables, the bridge surface itself… all have tension. Once again, engineers choose their materials wisely.

    Bending and torsion are two more unavoidable concerns for engineers. Imagine if the floors we walk over bent because of it: that would be an engineering failure. Or if we could rip doors off their hinges because of pushing high from the outside and low from the inside, causing torsion? Lastly, skyscrapers experience sheer forces in the wind because wind speeds are larger, the higher up from the ground. All kinds of things cause sheer forces, not just unexpected windstorms.

    Engineers compile tables of information comprising the strength of thousands of kinds of materials under these five force combinations. Then, they use that information in their calculations to ensure they don’t jeopardize lives and investments. Wise.

  • Gravity

    Einstein’s Approach to Gravity

    In the introductory material, we read that Einstein resolved some discrepancy within Mercury’s orbit. Well, he did, while providing the most accurate understanding we have of gravity, and being at the forefront of hair modeling.

    What did Einstein add to gravity, anyway?

    What if, instead of thinking of the masses as just sitting there on a (flat, constant) 3-dimensional grid of spatial coordinates, we imagine that the masses can warp the fabric of space itself? It’d be like putting bowling balls on a trampoline. That’s what happens to spacetime when stuff with mass exists in it: it warps.

    This idea is shown below with a two-dimensional coordinate plane, stretched into three dimensions.

    The more massive the object is, the deeper and steeper the space “funnel” it creates. Other nearby objects “roll down” the gravity funnel made by our original object. This “warped grid” view of gravity explains the warping of spacetime that occurs near black holes, and any other massive object. Light even bends around our own Sun.

    Newton explained the planets’ motion around the Sun using an invisible, attractive force called gravity. Einstein revolutionized this idea by saying the planets were following their paths in the fabric of the Sun’s general warping of space-time. Both claims lead to the same orbital motions observed in planets, etc. Einstein’s claims provide greater accuracy than Newton’s.

    It’s a mind-boggling concept, but it works great on paper. Not so much on fabric. Once Einstein makes an appearance rather than writing equations of motion for the objects, we change the mathematics so that they describes the space in which these objects exist itself. This way of thinking allows us to visualize what a singularity of infinite mass, known as a black hole, can do to the space around it. We’ll bring this up again later in physics, but for now, just imagine Aunt Gertrude ripping a hole in the trampoline. There’s no coming back from that. Fun time is over.

    Einstein’s Theory of General Relativity allows us to trace the evolution of space itself. It almost single-handedly gave birth to the science of cosmology, the study of the origin of the universe. Not to be confused with Cosmetology (the science of hair cutting), cosmology is a subject to which Einstein could have added to our understanding in addition to spacetime and relativity, two subjects he’s most known for. .

    Looking ahead of Newtonian physics, we point out that while gravity plays a central role in modern astronomy, astrophysics, and cosmology, it’s far too weak of a force in comparison with the electromagnetic and nuclear forces to be of any consequence in the world of quantum mechanics, another area of modern physics. However, don’t take that as a personal suggestion to ignore gravity when determining theories of skate boarding or skydiving baking.

    And don’t ignore Einstein’s general relativity and ideas on spacetime when accounting for our next planet’s orbit.