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A 2.50 kg rock is attached at the end of a thin, very light rope 1.45 m long and is started swinging by releasing it when the rope makes an 11° angle with the vertical. You record the observation that it rises only to an angle of 4.5° with the vertical after
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- In the figure, a solid cylinder M attached to a horizontal spring k (k = 3.00 N/m) rolls without 00000 slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these conditions the cylinder's center of mass executes simple harmonic motion with period 3M T = 2n. 2k where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical energy.) (Halliday, Resnick & Walker, 2011)arrow_forwardEngineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (the figure (Figure 1)). There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being tested on earth, but it is to be used on Mars, where the acceleration due to gravity is 3.71 m/s2. In the earth tests, when m is set to 13.0 kg and allowed to fall through 5.00 m, it gives 300.0 J of kinetic energy to the drum. If the system is operated on Mars, through what distance would the 13.0-kg mass have to fall to give the same amount of kinetic energy to the drum? How fast would the 13.0-kg mass be moving on Mars just as the drum gained 300.0 J of kinetic energy?arrow_forwardA simple pendulum is made of a 2 m-string and a bob of mass m. At t = 0, the pendulum is at its equilibrium position and is given an initial velocity v = 0.2 m/s. The maximum angular speed, O'max, is: O 0.1 rad/s O 0.8 rad/s O 0.4 rad/s 0.05 rad/s O 0.2 rad/s The equation of motion of a particle in simple harmonic motion is given by: x(t) = O 2cos(et) where x is in meters and tis in seconds At x = 0 the particle'sarrow_forward
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