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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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