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Work in 2D - Work in 2D Consider the pendulum shown in...

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Work in 2D Consider the pendulum shown in Figure 7.8. The pendulum is moved from position 1 to position 2 by a constant force F, pointing in the horizontal direction (see Figure 7.8). The mass of the pendulum is m. What is the work done by the sum of the applied force and the gravitational force to move the pendulum from position 1 to position 2 ? Method 1 - Difficult The vector sum of the applied force and the gravitational force is shown in Figure 7.9. The angle between the applied force F and the vector sum F t is a. Figure 7.9 shows that the following equations relate F to F t and F g to F t : Figure 7.9. Vector sum F t of F g and F. In order to calculate the work done by the total force on the pendulum, we need to know the angle between the total force and the direction of motion. Figure 7.10 shows that if the angle between the pendulum and the y-axis is [theta] , the angle between the total force and the direction of motion is [theta] + a. The distance dr is a function of d[theta]:
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