1. A simple pendulum is suspended from the ceiling by means of a string of length 2.18 m. Assume that there is no friction or air resistance. Suppose you were to release the pendulum from rest, starting from an angle of 38.3 degrees with respect to the vertical, as shown. What will be the speed of the pendulum at the instant it swings through its lowest point (that is, when it s momentarily hanging vertically)? 2. OK, once again we have a pendulum, this time of length 1.10 m, which you release from rest at an angle of 59.7 degrees to the vertical. What will be the speed of the pendulum at the instant it reaches an angle of 47.8 degrees above the vertical? 3. This, the length of the pendulum is 1.82 m. Now you start with the pendulum at 15.5 degrees with respect to the vertical, but rather than releasing it from rest, you give it a push downward. It swings to the other side, and reaches a maximum angle of 38.7 degrees with respect to the vertical. What must have been the initial speed of the pendulum just after you pushed it? 4. This time the pendulum is 1.04 m long. Suppose you start with the pendulum hanging vertically, at rest. You then give it a push so that it starts swinging with a speed of 1.29 m/s. What maximum angle (in degrees) will it reach, with respect to the vertical, before falling back down? 5. This time, the pendulum is 2.27 m long and has a mass of 3.53 kg. You give it a push away from vertical so that it starts swinging with a speed of 1.98 m/s. Due to friction at the pivot point, 1.00 Joule of the pendulum s initial kinetic energy is lost as heat during the upward swing. What maximum angle will it reach, with respect to the vertical, before falling back down?
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1. A simple pendulum is suspended from the ceiling by means of a string of length 2.18 m. Assume that there is no friction or air resistance. Suppose you were to release the pendulum from rest, starting from an angle of 38.3 degrees with respect to the vertical, as shown. What will be the speed of the pendulum at the instant it swings through its lowest point (that is, when it s momentarily hanging vertically)?
2. OK, once again we have a pendulum, this time of length 1.10 m, which you release from rest at an angle of 59.7 degrees to the vertical. What will be the speed of the pendulum at the instant it reaches an angle of 47.8 degrees above the vertical?
3. This, the length of the pendulum is 1.82 m. Now you start with the pendulum at 15.5 degrees with respect to the vertical, but rather than releasing it from rest, you give it a push downward. It swings to the other side, and reaches a maximum angle of 38.7 degrees with respect to the vertical. What must have been the initial speed of the pendulum just after you pushed it?
4. This time the pendulum is 1.04 m long. Suppose you start with the pendulum hanging vertically, at rest. You then give it a push so that it starts swinging with a speed of 1.29 m/s. What maximum angle (in degrees) will it reach, with respect to the vertical, before falling back down?
5. This time, the pendulum is 2.27 m long and has a mass of 3.53 kg. You give it a push away from vertical so that it starts swinging with a speed of 1.98 m/s. Due to friction at the pivot point, 1.00 Joule of the pendulum s initial kinetic energy is lost as heat during the upward swing. What maximum angle will it reach, with respect to the vertical, before falling back down?
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