PhySP18SS6.3.1 Truss static problems are notoriously mean and nasty in Physics. Here is a short cut that comes in handy for “y shaped” connections.
PhySP18SS6.3.2 You can turn the force vectors into a scalene triangle using a little “parallel lines cut by a transversal” geometry to help you determine the angles. Once you have the angles and one force vector, you can determine what the other two forces are by employing the “Law of Sines”.
PhySP18SS6.3.3 Here is an extreme case of a y shaped truss problem. The tensions in the cables go to infinity as the angle gets really small.
PhySP18SS6.3.4 Inclined planes. You must tilt your axis to save you a lot of pain. Typical strategy for solving these: carefully draw FBD (tile axis), then ∑F= max, then one of the orange kinematic equations.
PhySP18SS6.3.5 Elevators are a favorite of Physicists because they go from Inertial Frames of Reference to noninertial frames of reference if you push the up the up or down button. By doing that you cause the system you are standing in to accelerate. When the system you are engaged in accelerates and you don’t know it’s accelerating, it is considered a non inertial frame of reference. Normal physics won’t work for you. For instance, when you hit the up button in an elevator you feel like you just gained 20 lbs (magic?, no just acceleration)
PhySP18SS6.3.6 Same thing as previous screen shot shown a slightly different way.
PhySP18SS6.3.7 Some numbers in the elevator equation.
PhySP18SS6.3.8 What is the cable breaks. Einstein had one of his happiest thoughts when he went through this thought experiment.
PhySP18SS6.3.9 The old alien trick. They can fool you that you are back on earth if they hook up a cable to your floating elevator in interstellar space and start dragging your frame of reference with an acceleration of 9.81m/s/s. You will think you are back on earth, open the door and . . . be introduced to the vacuum of space. sucka!
PhySP18SS6.3.10 Here is another example of a noninertial frame of reference. If the train car is accelerating Unbeknownst to you, you will think there is a ghost in there with you because that ball hanging from the ceiling will mysteriously hang at an angle.
PhySP18SS6.3.11 So Einstein said . . . Is it gravity or acceleration? THey are essential equivalent. This is one of the main principles of General Relativity
PhySP18SS6.3.12 Is she on earth or just accelerating in space.
PhySP18SS6.3.13 Did that ball drop because he is on Earth or because he is accelerating upward?
PhySP18SS6.3.14 . . .
PhySP18SS6.3.15 This also sort of makes you think about the bending of light. Turns out . . . it DOESN’T really bend. Either the space-time continuum is curves and light is just following the most “horizontal” path available or the reference frame is accelerating upward so light APPEARS to bend. So Newton’s 1st Law (law of inertia) still holds. The light in motion DOES stay in motion in a straight line. It can’t help it that stupid spacetime is bending into massive objects.
PhySP18SS6.3.16 . . .
PhySP18SS6.3.17 Inclined planes. Always tilt your axis and always show your right triangles. Did I ever tell you that a vector at an angle is the hypotenuse of a right triangle?
PhySP18SS6.3.18 same problem.
PhySP18SS6.3.19 A little more complicated. TWO angles.
PhySP18SS6.3.20 The Atomic Chemistry of Friction. On a picometer scale.
PhySP18SS6.3.21 Electrons are really little negative charged bbs like you learn in chemistry. That is a convenience model. Electrons are more like packets of wavelike energy which can only have quantized fundamental frequencies. High energy Electrons can be represented by a short and tight autocorrelated wavelet (top drawing) containing a lot of fundamental frequencies or a lower energy electron can be represented by a more spread out combination of lower fundamental frequencies. The point is, the electron’s location is hard to pin down (part of Heisenberg’s Uncertainty Principle) The more you know about the momentum of the electron, the less you know about the position and vice versa. So these electrons are represented by probability clouds (those shapes you learn in Chemistry). The point is, we don’t really know where any given eelectron is at any given time. Ok, keep that in mind.
PhySP18SS6.3.22 The orbitals of the electrons act like shields around the positive nest of protons in the nucleus. but those shields are not solid. Remember, these electrons are moving around in unpredictable ways so sometimes some of the positive force of the nucleus leaks out beyond the atomic surface of the outermost atoms of a surface.
PhySP18SS6.3.23 This “leakage of + charge” from the proton nest causes the outer electrons in the other surface to move up (because they are attracted to the positive force). They don’t jump the gap, but they do cause that area of the bottom surface to become partial negatively charged. This positive negative attraction is the source of all friction. We call these random temporary attractions between surfaces London Dispersion Forces (LDFs) They were discovered by a scientist with last name London in 1931.
PhySP18SS6.3.24 So why is water such a good lubricant (as you may have noticed if you hav e ever slipped on a slick tile floor)?
PhySP18SS6.3.25 The oxygen of the H2O holds onto the electrons to strong. There are not a lot of loose electrons in a set of water molecules, therefore not as much of a chance for LDFs
PhySP18SS6.3.26 Hydrogen “Bonds” are just about the strongest INTERMOLECULAR bonds there are. That’s why water dominates your body and the world.
PhySP18SS6.3.27 H-Bonds are Dipole-Dipole
PhySP18SS6.3.28 This a micrometer scale view. In a static situation the peaks of one surface settles down into the valleys of another surface. This makes the outer atoms of each surface close enough to each other for many LDFs to form (see Coulomb’s Law).
PhySP18SS6.3.29 So we call this static arrangement between surfaces peak to valley. Look at all those purple LDFs.
PhySP18SS6.3.33 What is two surfaces were perfectly smooth? Then there wouldn’t be any friction right? WRONG!! The friction would skyrocket. Look at all those LDFs forming becasue the surfaces are soooo close to each other. Good luck breaking these two surfaces apart.
PhySP18SS6.3.34 by definition. Notice that the mu sub s and mu sub k are COEFFICIENTS (no units) because the Newtons over Newtons cancel.
PhySP18SS6.3.35 . . .
PhySP18SS6.3.36 Eventhough there are LDFs in both cases above we only show the friction force on the incline because you don’t show a force on a FBD if it has a particular direction. If I tilt a surfac e and the block does not move, the static friction opposes potential motion and now it has a particular direction. See, it needed a purpose to show up. Is that true for all of us? Sorry, getting a little worn out.
PhySP18SS6.3.37 Angle of Repose is the angle of an incline where whatever is sitting on the incline is “JUST ABOUT TO SLIP”.
PhySP18SS6.3.38 We did a theta rep (angle of repose) little 5 minute activity between rough steel and smooth steel and found the thea rep to be about 17°. Now, here’s the cool thing. From knowing that, we can find the coefficient of static friction between the two surfaces.
PhySP18SS6.3.39 some data
PhySP18SS6.3.40 so we need to get from this FBD to the formula at the bottom right.