7.85. Set Up: At any point, the potential energy is given by where l is the string length and is the angle the string makes with the vertical. At the top of the swing, the kinetic energy is zero while the potential energy is a maximum since whereas, at the bottom of travel, the kinetic energy becomes a maximum equal to the of the top of the swing. In terms of conservation of energy, or where “f “ refers to the vertical position of the pendulum and “i “ refers to top of travel. Solve: Solving for the velocity, The tension in the string at this instant is found using a force balance of the weight and radial acceleration, Reflect: As the string passes through the vertical the ball has an upward acceleration, due to its circular motion. Therefore, there is a net upward force and the tension is greater than the weight of the ball. 7.86. Set Up: Since Let at the lowest point in a swing. Then and as shown in the sketch. Solve: (a)
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