2. Clock P and clock Q leave the spatial origin of an inertial frame S at time t
ID: 1884448 • Letter: 2
Question
2. Clock P and clock Q leave the spatial origin of an inertial frame S at time t 0, defining the origin event O. Both clocks move along the + axis, with clock P originally traveling at a speed of 0.800c, while Q travels at a speed of 0.200c. After a while, however, clock P decelerates, comes to rest, and then begins to move back toward the origin. A short time later, clock P collides with clock Q, defining event A (a) Construct a qualitatively accurate, spacetime diagram depicting the sequence described above, labeling worldlines and events (b) Assume that clocks P and Q were both synchronized with the clock at the origin of frame S when they left the origin. Will P and Q necessarily read the same value when they collide? Explain. (c) Observers in frame S measure the time between events O and A with a pair of synchronized clocks (at the spatial locations of each event). Clocks P and Q each also register a time between these events. Which of the clocks or pairs of clocks measures the coordinate time interval? Which measures the proper time? Which measures the 1/c times the spacetime interval? Describe your reasoning, and remember that clocks can measure none, one, two, or all three of the different kinds of time.Explanation / Answer
Fluids are characterized by their ability to flow. In somewhat technical language, a fluid is any material that can't resist a shear force for any appreciable length of time. This makes them hard to hold but easy to pour, stir, and spread. Fluids have no definite shape but take on the shape of their container. (We'll ignore surface tension for the time being. It's really only significant on the small scale — small like the size of a drop.) Fluids are polite in a sense. They yield their space relatively easily to other material things; at least when compared to solids. A fluid will get out of your way if you ask it. A solid has to be told to get out of the way with destructive force.
Fluids may not be solid, but they are most certainly material. The essential property of being material (in the classical sense) is to have both mass and volume. Material things resist changes in their velocity (this is what it means to have mass) and no two material things may occupy the same space at the same time (this is what it means to have volume). The portion of the drag force that is due to the inertia of the fluid — the resistance that it has to being pushed aside — is called the pressure drag (or form drag or profile drag). This is usually what someone is referring to when they talk about drag.
Recall Bernoulli's equation for the pressure in a fluid…
P1 + gy1 + ½v12 = P2 + gy2 + ½v22
The first term on each side of the equation is the part of the pressure that comes from outside the fluid. Typically, this refers to atmospheric pressure weighing down on the surface of a liquid (not relevant right now). The second term is the gravitational contribution to pressure. This is what causes buoyancy (also not relevant right now). The third term is the kinetic or dynamic contribution to pressure — the part related to flow (very relevant right now). This will help us understand the origin of pressure drag.
Start with the definition of pressure as force per area. Solve it for force.
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