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A cylinder of radius r and mass m rolls without slipping on a fixed cylinder of radius R. Obtain the
Lagrange’s equation of motion for short period of time before the cylinder separates.
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- Problem 5: Two blocks are connected with a rope as shown. The surfaces and the pulley are frictionless. The pulley is a disk with radius r and mass m,. A force F is applied to Mass 1 as F m1 shown so that Mass 1 accelerates to the left and Mass 2 accelerates upward. Take the positive direction to the be the direction of accelerations of the masses. (That is, the positive direction for Mass 1 is to the left, and the positive direction for Mass 2 is upward.) mp m2 In the space below, show how you would find the acceleration of the masses. Start with equations from the equation sheet and show your steps to the point where you would calculate the results. You do not need to calculate any numerical result. Just show how you would solve the problem. Be sure your equations reflect the positive direction as described above. Max characters allowed 3000. 0/3000A cord of negligible mass is wrapped around the outer surface of the 50-lb cylinder and its end is subjected to a constant horizontal force of P = 2 lb as shown in (Figure 1). Take r = 0.9 ft. Figure 1 of 1 P = 2 lb Part A If the cylinder rolls without slipping at A, determine its angular velocity in 5 s starting from rest. Neglect the thickness of the cord. Express your answer in radians per second to three significant figures. IVE ΑΣΦ | 11 Submit Request Answer < Return to Assignment vec Provide Feedback p ? rad/sThe Earth orbits the Sun in a near circular orbit of radius 1.5 × 1011m. Find themagnitude of Earth’s velocity, angular velocity, and circular acceleration as itorbits the Sun. Hint: You already know the period of this orbit. A car starts from rest on a curve with a radius of 120 m and acceleratedtangentially at a constant 1.0 Τm s2. Through what angle will the car havetravelled when the magnitude of its total acceleration is 2.0 m/s2?