3. A Kicked Baton. 20 minutes. 15 points. Two identical masses m are connected by a...
7. Two Connected Toy Train Cars. 15 minutes. 10 points Two identical masses m on frictionless and massless wheels are moving along the r direction and connected by a spring of force constant k. The equilibrium separation is d. (a) Write the Lagrangian of the system in terms of the positions of the two masses. (b) Transform the Lagrangian to the Hamiltonian, explaining what you do. (c) Obtain Hamilton's equations for this system. You are not asked to solve them....
Problem 1 Two identical pucks, each of inertia m, are connected to a rod of length 2r and negligible inertia that is pivoted about its center (that is, there is some sort of pin though its center, around which it can rotate without friction). A third puck of inertia m/2 strikes one of the connected pucks perpendicular to the rod with a speed vi. Assume the collision is elastic. (a) Draw a diagram of the situation, clearly labeling the direction...
QUESTION 1 A dumbell consists of two identical masses of mass M attached to a either end of a rod of length 2X and of negligible mass. If the dumbell is rotated about an axis perpendicular to the rod and passing through the middle of the rod, as shown in the diagram. What is the rotational inertia of the dumbell? Axis. -*-X ←-ㄧㄧㄨ 2Mx2 2M2x MX2 M2x QUESTION 2 Two identical uniform thin rods of length 0.542 m and mass...
10. + 0/3 points | Previous Answers SerPSET9 12.P.021. My Notes + Ask Your Teacher John is pushing his daughter Rachel in a wheelbarrow when it is stopped by a brick 8.00 cm high (see the figure below). The handles make an angle of a = 20.0° with the ground. Due to the weight of Rachel and the wheelbarrow, a downward force of 405 N is exerted at the center of the wheel, which has a radius of 15.0 cm....
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...