Vhen we do dimensional analysis, we do something analogous to stoichiometry, but with multiplying instead of adding. Consider the diffusion constant that appears in Fick's first law: dn J=-D dx n this expression, J represents a flow of particles: number of particles per unit area per second, n represents a concentration of particles: number of particles per unit volume; and x represents a listance. We can assume that they have the following dimensionalities: • ) = 1/L2T • [n] = 1/L3 • [x] = L From this, determine the dimensionality of D. (h) Einstein discovered a relation that expresses how D depends on the parameters of the system: the size of the particle diffusing (R), the viscosity of the fluid it is diffusing in w,and the thermal energy parameter (kg 7). These have the dimensionalities • [kg 7] = ML2/T2 • ) = M/LT • [R] = L Assume that we can express Das a product of these three quantities to some power, like this: D= (kg na (b (R)C Vrite eauations for a, b, and c that will guarantee that D will have the correct dimensionality for M, L, and T. (i) In this case, there were exactly the right number of parameters to give the same number of equations as there were unknowns. That will not always be the case, but sometimes his method still can be made to work by adding physical knowledge about the dependences. Solve these equations and write an expression how D depends on the three parameters. (The correct equation has a factor of 1/(6n) that cannot be found from dimensional analysis. Make sure to nclude this factor in vour answer.)

A block rests: Part G | Problem A block, m1 = 5 kg, rests on a horizontal, frictionless surface. A rope connected to the block is draped over a uniform, solid disk (a pulley) of mass m, = 2 kg; and the rope is connected at its other end to a hanging mass, m2 = 10 kg. When the block is released from rest, we wish to determine information about each block, such as their accelerations, distances traveled after a given amount of time, etc... mp m1 m2 How many revolutions does the pulley make during this 2 seconds? 115

Part F Now determine m₁a₁y = Σ Fly, the sum of the y components of the forces acting on block 1. Take forces acting upward as positive. Express your answer in terms of some or all of the variables T, m₁, and g. VE ΑΣΦ m1aly = Σ Fy = Submit Request Answer ?

When a 60 kg skier first starts to be pulled up the ski hill by an old school T-bar, she undergoes a constant acceleration of 1.8 m/s2 during the first few seconds of the pull.  The applied force from the T-bar is directed 40 degrees above a line that is parallel to the surface of the hill  The incline of the hill is 19 degrees above the horizon, as can be seen by alpha in the figure below.  Assume that the positive X direction is directed up the hill and the positive y direction is directed away from the surface of the hill and that the coefficient of dynamic friction between the skiis and the snow is 0.1.  a) What is the magnitude of the applied force (FApp) in Newtons (N) required from the T-bar when the skier first starts to be pulled up the hill with a constant acceleration of 1.8 m/s2?  b) What is the magnitude of the normal force between the skier and the snow in Newtons (N) in the scenario described above (skier is being pulled up the hill by the T-bar with a constant…