A simple pendulum consists of a 0.8-kg bob connected to a massless inextensible cord with a length L = 1.1 m. The bob is set into motion and its angular displacement is given by 0(t) = 0.11cos(wt), where 0 is in radians and t is in seconds. Take g = 9.8 m/s^2, determine the mechanical energy of this %3D pendulum. 0.085 J O 0.066 J 0.052 J

Engineers 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?

While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every T = 6.6 seconds. Frequency is = 1/6.6 Angular Velocity = 0.952 Length of the chandelier = 10.81 That evening, while hanging out in J.J Thompson's House O' Blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the Michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is T + 0.11 Seconds. Determine the acceleration due to gravity in m/s^2 at the club

7. A 5.00-kg solid ball of radius 0.250 meters is pressed back against a spring having a spring constant of 1625 N/m, compressing the spring by 20.0 cm. The solid ball is released, and the object rolls 1.00 meter on a frictionless horizontal surface (without slipping) and then rolls up a rough 3.00 meter long incline plane (with an angle of 10.0 degrees to the horizontal). The ball eventually comes to rest at the top of the incline plane. When the ball rolls down the incline plane and compresses the spring, how much will the ball compress the spring? 3.00 m 1.00 m