4) (a) A 1-D infinite potential well of width a contains two spinless particles, each of mass m. The potential representing the interaction between the particles V = a8(x1 = x2). Calculate the ground state energy of the system corrected to first order in A.
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- 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 tube 1.30 m long is closed at one end. A stretched wire is placed near the open end. The wire is 0.357 m long and has a mass of 9.50 g. It is fixed at both ends and oscillates in its fundamental mode. By resonance, it sets the air column in the tube into oscillation at that column's fundamental frequency. Assume that the speed of sound in air is 343 m/s, find (a) that frequency and (b) the tension in the wire. (a) Number i 66.0 (b) Number i Units Hz UnitsNone
- (b) An electric dipole consists of a charge of -10 pC at position (0, -1, 0) mm and +10 pC at position (0, 1, 0) mm. (i) (ii) Express its dipole moment as a vector [6 marks] Find the components of E in the directions of the x, y and z axes at the points with position vectors (4, 0, 0) mm and (0, 4, 0) mm1) Given the sinusoidal voltage v(t) 50 cos(30t + 10°) V, find: (a) the amplitude Vm, (b) the period T, (c) the frequency f, and (d) v(t) at t= 10 ms.SITUATION 1 (Fluid Flow in a Closed Conduit) Consider a fluid, with density (p) of 998.21 kg/m³ and dynamic viscosity (u) of 1.002 x 103 N-s/m², flowing in a 2000-meter long, 50-mm diameter smooth round pipe with velocity of 2.5 m/s. The energy loss on the pipe flow (he) due to friction between the pipe and the fluid is determined using Darcy-Weisbach equation, given as h₁ = f (²) (1/1) where f is the friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the velocity of the flow, and g is the gravitational acceleration. The friction factor may be determined using an empirical equation developed by Nikuradse for flow in smooth pipes, given as 1 =0.869 In (Re√7)-0.8 where Re is the Reynolds number of the flow, determined as VDp R₂ = μl The friction factor equation given is only valid for flows with Reynolds number higher than 4000 (turbulent flow). Guide Questions: Determine the Reynolds number of the flow. Is the Nikuradse equation for friction factor…
- 1) A 0.1 kg object oscillates as a simple harmonic motion along the ? −axis with a frequency ? = 3.185 Hz. At a position ?1 , the object has a kinetic energy of 0.7 J and a potential energy 0.3 J. The amplitude of oscillation, ?, is: (a) 0.12 m (b)0.22 m (c) 0.31 m (d)0.42 m 2) A block of mass m is attached to a spring with force constant, ? and oscillate at a frequency ?. If the mass is changed to ?′ = ?/2, and the spring force is changed to ? ′ = 2?, then the new frequency ?′ of the oscillation would be, (a) ?′ = 2? (b)?′ = ? (c) ? ′ = ?/2 (d)?′ = 4? The following given is for questions 3 and 4: A block of mass ? = ? kg is attached to a spring with spring constant ? = ??? N/m, and set to oscillates on a frictionless horizontal surface. At time ? = ? its position is ?? = ? and its velocity is ?? = +? m/s. 3) Which of the following is true about the oscillation amplitude and the phase constant, : (a)A = 0.5, 2 (b)A = 0.5, 2 (c) A = 0.25,…For an object of mass m=3 kg to slide without friction up the rise of height h=1 m shown, it must have a minimum initial kinetic energy (in J) of: h O a. 40 O b. 20 O c. 30 O d. 10I need the answer as soon as possible
- 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/s2. Heat conduction in a square plate Three sides of a rectangular plate (@ = 5 m, b = 4 m) are kept at a temperature of 0 C and one side is kept at a temperature C, as shown in the figure. Determine and plot the ; temperature distribution T(x, y) in the plate. The temperature distribution, T(x, y) in the plate can be determined by solving the two-dimensional heat equation. For the given boundary conditions T(x, y) can be expressed analytically by a Fourier series (Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 1993):09.......
