3) The contour of a bumpy road is approximated as: y(x) = 0.03 sin (0.125x) m. What is the amplitude of the vertical acceleration of the wheels of an automobile as it travels over this road at a constant horizontal speed of 40 m/s?
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- 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 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?Typing clear i will give 5 upvotes
- 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).= 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.In the month of June, Jose Hebert's Beauty Salon gave 4,200 haircuts, shampoos, and permanents at an average price of $40. During the month, fixed costs were $16,700 and variable costs were 75% of sales. Your answer is partially correct. Determine the contribution margin in dollars, per unit and as a ratio. (Round contribution margin per unit and contribution margin ratio to 2 decimal places, e.g. 5.25 & 10.50.) Contribution margin %24 41750.00 Contribution margin per unit 2. 10.00 25 Contribution margin ratio
- In the diagram shown below, the four currents are assumed to be held in place at their current locations. The currents have the following values: IA = 3.000 A, IB = 3.000 A, Ic 1.000 A and ID 2.000 A. Let d = 12.500 cm and assume standard x- and y-axes at point P1. (Be careful about signs!) AO 3d The magnitude of the total magnetic field at point P1, in μT and to three decimal places, is d P1Suppose 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?Physics
- 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 structureAn electron is accelerated through a potential difference of 1.5 MV and hence gains 1.5 MeV of energy. Find its final speed and momentum. (me 9.11^10-31 kg) explain step, by step and remember it is a relativistic problemWhat is the cost, c, of a call of m minutes duration? Write the equation in both point-slope and slope-intercept form.