Using a rope, you pull a friend sitting on a swing (Figure 10.16).

(a) As you increase the angle \(\theta\), does the magnitude of the force \(\vec{F}_{\mathrm{rp}}^{c}\) required to hold your friend in place increase or decrease?

(b) Is the magnitude of that force larger than, equal to, or smaller than the magnitude of the gravitational force \(\vec{F}_{\mathrm{Fp}}^{G}\) exerted by Earth on your friend? (Consider the situation for both small and large values of \(\theta\).)

(c) Is the magnitude of the force \(\vec{F}_{\mathrm{sp}}^{c}\) exerted by the swing on your friend larger than, equal to, or smaller than \(F_{\mathrm{Ep}}^{G}\) ?

Data from Figure 10.16

Figure 10.16 Example 10.2. suspension point-