The two blocks of Figure 6.17 are attached to each other by a massless string that is wrapped around a frictionless pulley. When the bottom 4.00-kg block is pulled to the left by the constant force P, the top 2.00-kg block slides across it to the right. Find the magnitude of the force necessary to move the blocks at constant speed. Assume that the coefficient of kinetic friction between all surfaces is 0.400.
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- 2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…Problem 2 Write a computer program that can be used to determine the magnitude and the point of application of the resultant of the vertical forces P1 , P2, ..., P, that act at points Aj , A2, ..., An that are located in the xz plane: P2 Pn P1 An NDesign a wide flange W column 8 m in height to support an axial dead load of 1000 kN and a live load of 1200kN in the interior of a building. The column base is rigidly fixed to the footing and the top of the column isrigidly framed to very stiff girders. Assume that bracing is provided to prevent side sway in the weak axis/planeof the column (you don’t have to consider slenderness in this direction), but side sway is not prevented aroundits strong axis. Select an economical W shape.
- A uniform Simply-supported beam is found to vibrate in its first mode with the amplitude of 12 mm at its center. Assume E=200 GPa, I = 1000 mm“ , p=7500 kg/m², A=50mm² and L=2 m. Determine the maximum bending moment in the beam. Also find the first three natural frequencies.4. The outer facing of a room is constructed from 0.75 m thick brick, 25 cm of mortar, 12 cm of limestone (k=0.186 W/mK) and 0.5 m of plaster (0.096 W/mK). Thermal conductivities of mortar and brick are both 0.52 W/mK. Assume that the heat transfer coefficients on the inside (plaster side) and outside (brick side) surfaces of the wall to be 8 and 24 W/(m^2 K), respectively. Calculate the overall coefficient of heat transfer (W/(m^2 K). Show your solutionA beam containing 1000 monoenergetic photons applied to material with a thickness of 0.5cm and linear attenuation coefficient of 82 x 1 m-1. Find the number of outgoing beam.
- An aluminum wire having a cross-sectional area equal to 4.60 x 10-6 m? carries a current of 7.50 A. The density of aluminum is 2.70 g/cm³. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. 1.95E-4 The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm/sQ.4 In an experimental setup, mineral oil is filled in between the narrow gap of two horizontal smooth plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these temperatures, ONLY the radiative heat flux is negligible. The thermal conductivity of the oil does not vary perceptibly in this temperature range. Consider four experiments at steady state under different experimental conditions, as shown in the figure Q1. The figure shows plate temperatures and the heat fluxes in the vertical direction. What is the steady state heat flux (in W m) with the top plate at 90°C and the bottom plate at 45°C? [4] 30°C 70°C 40°C 90°C flux = 39 Wm-2 flux =30 Wm2 flux = 52 Wm 2 flux ? Wm-2 60°C 35°C 80°C 45°C Experiment 1 Experiment 2 Experiment 3 Experiment 4Electromagnetic Pulse propagating at oblique angle to a dielectric interface Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2. Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse. e.g., n1 = 1 , n2 = 2 initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L). For the slope of the interface, one could choose m = 1.
- Two circular shafts AB and BC of the same material but different diameter are welded together at point B as shown in the figure. Ends A and C are fixed. An external torque T, is applied to the shafts at point B. Find the torques exerted on the ends of the shafts at A and C.A bicycle wheel has a diameter of 64.6 cm and a mass of 1.87 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 125 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 8.96 cm diameter sprocket if the wheel is to attain an acceleration of 4.49 rad/s22? (b) What force is required if the chain shifts to a 5.57 cm diameter sprocket?We wish to coat a glass surface with an appropriate dielectric layer to provide total transmission from air to the glass at a free-space wavelength of 570 nm. The glass has refractive index n3 = 1.45. Determine the required index for the coating and its minimum thickness