7.43 *** (Computer] Consider a massless wheel of radius R mounted on a frictionless horizontal axis. A point máss M is glued to the edge, and a massless string is wrapped several times around the perimeter and hangs vertically down with a mass m suspended from its bottom end. (See Figure 4.28.) Initially I am holding the wheel with M vertically below the axle. At 1 = 0, I release the wheel, and m starts to fall vertically down. (a) Write down the Lagrangian L = T - U as a function of the angle o through which the wheel has turned. Find the equation of motion and show that, provided m < M, there is one position of stable equilibrium. (b) Assuming m < M, sketch the potential energy U () for -n < ¢ < 47 and use your graph to explain the equilibrium position you found. (c) Because the equation of motion cannot be solved in terms of elementary functions, you are going to solve it numerically. This requires that you choose numerical values for the various parameters. Take M = g = R = 1 (this amounts to a convenient choice of units) and m = 0.7. Before solving the equation make a careful plot of U ($) against o and predict the kind of motion expected when M is released from rest at ø = 0. Now solve the equation of motion for 0 < t < 20 and verify your prediction. (d) Repeat part (c), but with m = 0.8.

Hello. Answer is s=0.42m (how far the spring goes down before stopping the object falling). I am uploading this question as the example answer's working out was bad I find it hard to follow. I would like to see working out how the calculations equate to the answer being s=0.42m

In a nutshell, a smaller rock is propelled into the air as a huge counterweight in the back falls down, effectively converting gravitational potential energy into kinetic energy for the rock and the weight. But, since the rock is smaller.. it is propelled at a much faster velocity! Let's say we wanted to hurl a 50 kg boulder at a castle wall 100 meters away. Our wooden structure for the trebuchet is 10 meters tall, so that is the maximum distance the counterweight can fall. Assuming the launch angle is a perfect 45 degrees, and the boulder is released from ground level, derive the needed mass of the counterweight that will give the boulder enough kinetic energy to reach the base of the castle walls. You may assume no energy is "lost" due to friction, and ALL the counterweight's gravitational potential energy is converted into the boulder's kinetic enerqy. (HINT: You will need to employ 2D kinematics to find the needed final velocity, then use that final velocity in an energy equation…

Where can i get the solution of Vector Mechanics For Engineers:Dynamic 12th SI units (written by beer) for free??