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Question1
Adjust the solution process discussed in class for uniform slow viscous flow past a sphere to the case of flow past a circular cylinder. a. start with the 3D Navier-Stokes equations for viscous flow. Non dimensionalize system, let Re → 0 and formulate the pde problem for the stream function in polar coordinates ψ(r,θ). b. answer the pde problem using separation of variables by letting ψ(r,θ)=F(r)G(θ). Use the boundary conditions far away from the cylinder to decide a functional form for G(θ) and reduce the pde to an ode for F(r). c. answer the ode for F(r). Show that the boundary conditions far away from the cylinder cannot be fulfilled. d. Cancel the fastest growing term of F(r) and determine the velocity field. Is the answer appropriate near the cylinder? e. The failure of the solution at infinity is known as Stokes' paradox. Give a probable description for why the solution fails.
A photon of energy E collides with an electron at rest. Calculate the maximum amount of energy Ek that may be transfered to the electron. Make a graph of Ek versus E, labeling the scale in electron volts.
An arrow is fire with a speed of 20m/s at the block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it.
A projectile is launched from the top of a cliff above level ground. At launch the projectile is 35 meters above the base of the cliff and has the velocity of 50 meters per second at an angle 37° with horizontal. Air resistance is negligible.
A capacitor consists of a set of two parallel plates of area A separated by a distance d. find the magnitude of the charge on the plates
If linear momentum is conserved when there is no external force applied, how is angular momentum conserved
A circuit employs a silicon solar cell to detect flashes of light lasting 0.25 s. what is the minimum power of a flash of light of wavelength
A resistor, capacitor and inductor are connected in series to an ac source with a frequency of 30 Hz and an rms potential of 40 V. What is the resonance frequency for this circuit
An electromagnetic wave travelling the +z direction has a maximum magnetic field of 10^-7 T in the negative y direction at z = 0 and t = 0. The magnetic field falls to zero in 3 x 10^-16 seconds.
A horizontal merry-go-round has a mass of 1000 kg, and is a solid disk of radius 2.00 m. It is started from rest by a constant horizontal force of 50.0 N applied tangentially to the edge of the disk.
A large boulder rests on a cliff 500 m above a small village in such a position that, What is the initial speed of the boulder
One hockey puck of mass 0.2 kg strikes an identical stationary puck on a frictionless ice rink. what fraction of the energy was lost
A solid sphere of mass 4.4 kg and radius 0.12 m is at rest at the top of a ramp inclined 15°. Find the sphere's total kinetic energy when it reaches the bottom
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