Chapter 7, Problem 86GP

A simple pendulum consists of a small object of mass m (the “bob”) suspended by a cord of length ℓ (Fig. 7–32) of negligible mass. A force $\stackrel{\to }{F}$ is applied in the horizontal direction (so $\stackrel{\to }{F}=F\hat{i}$), moving the bob very slowly so the acceleration is essentially zero. (Note that the magnitude of $\stackrel{\to }{F}$ will need to vary with the angle θ that the cord makes with the vertical at any moment.) (a) Determine the work done by this force, $\stackrel{\to }{F}$, to move the pendulum from θ = 0 to θ = θ₀. (b) Determine the work done by the gravitational force on the bob, ${\stackrel{\to }{F}}_{\text{G}}=m\stackrel{\to }{g}$, and the work done by the force ${\stackrel{\to }{F}}_{\text{T}}$ that the cord exerts on the bob.

FIGURE 7–32

Problem 86.