Two masses are connected to a string and hung on a pulley to make an atwood machine. The masses are different values such as M > m. The setup is shown. Assume the string is massless and the pulley is ideal. When the masses are gently released, there is a resulting acceleration. Which of the following equations will calculate the mass of m in the system if the big mass and acceleration are known? A) m = 2M(a/g). B) = m 2M(g/a). C) m = M(g- a/g+a). D) m = M(g+a/g -a).
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- The force of a spring obeys Hooke's law: F = -kx for some positive constant > 0, where x = x(t) measures the displacement from its rest position of a particle of mass m > 0 attached to the spring. i. Use Newton's Second Law to show that the equation of motion of the particle is +w²x=0. Determine w in terms of k and m. Find the solution to this equation if the particle is released at time t 0 from position x = 4 with = velocity 2w. ii. Show that = 1 w2 E = + 2 is a conserved quantity of the motion. What is the value of E for the above solution. What is the meaning of the two terms on the right hand side?A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i+ 3xyj + 3y2k. Use Stokes' Theorem to find the work done.= The figure shows a horizontal beam of mass M = 59.1 kg and length L = 6.4 m supported at its left end by a frictionless pin and at the other end by an ideal cable attached to wall h 4 m above the beam. A mass m = 22.1 kg is suspended from the beam a distance d = 2 m from the wall. Find the tension in the cable. T h d→ m M L = _ N Report your numerical answer below, assuming three significant figures. Remember to include a as necessary.
- Shown at right are two boxes (mass m and 2m) attached to identical springs, and attached to each other by a string running over a pulley. The springs are initially neither stretched nor compressed and the masses are initially at rest. The blocks then speed up and eventually slow down again until each block has moved a distance s, at which point both blocks are momentarily at rest. Determine a symbolic expression in terms of given variables for the spring constant of each identical spring. No explanation necessary. We'll use the work-energy theorem with a system consisting of both blocks, the string, both springs, and the Earth. The net external work on this system is zero (the various normal forces all act on points of contact that are not moving). The initial and final kinetic energy for both blocks is zero because they are not moving 2m m ΔΕ = 0 ks² · − 0 + ¼½ks² − 0 + mgs − 0 + (−2mgs) − 0 = 0 k = mg SIn the figure below, a metal bar sitting on two parallel conducting rails, connected to each other by a resistor, is pulled to the right at a constant speed. The resistance R = 6.00 Q, the distance between the rails is { = 1.20 m, and a uniform 2.30 T magnetic field is directed into the page. At what speed (in m/s) should the bar be moved to produce a current of 0.500 A in the resistor? R Fapp m/sPlease step by step solutions
- Suppose there is now friction and the equation of motion becomes x+2yx+w²x = 0, where 0 is some constant of friction. γ i. Find the general solution for x(t), under the assumption that w. You do not need to impose initial conditions here. ii. What is the range of for which the above solution is (1) heavily damped; (2) lightly damped. What happens to the above solution and the physical system when y = w?A system is described by the action S[r, r'] = [ dt (x² + 4rª + mr³4), r(t) where m is a constant. Find the Euler-Lagrange equation for r = which extremises S. Interpret each of the terms that appear in the Euler- Lagrange equations in terms of Newton's second law. Find a conserved quantity for this system.Vishnu
- In the context of of cubic interpolation as discussed in the lecture, in order to find the cubic interpolating line one must use parsimonious methods solve a linear system where the unknow variable is time. must solve a linear system in two equations a two varibles. select four rates. solve a cubic system. solve a cubic system of four equations in four variable where the unknown is time select two rates find the slope and the intercept of the interpolating line ☐ approximate the term structureWrite the balanced chemical equation for the complete, stoichiometric combustion of ethylene in (a) nitrous oxide and (b) air. Compare the required number of moles and the oxidizer mass using each of the two oxidizers for the complete, stoichiometric combustion of ethylene. Use the following Matlab code to solve 3. Put in your own equations and supply the initial guess values.The two-dimensional wave equation describing the vibrations of an infi- nite string is Θη Ot2 2021 მ2 where n = n(x,t), — -x 0 is a constant. Its general solution can be written as n(x,t) = F(x-ct) + G(x + ct), with F and G arbitrary smooth functions. If at time t = 0 the shape of the string is n(x, t = 0) at 9 = 5+x4 and the string is released with velocity (x, t = 0) = 0, determine n(x,t) for t > 0.