Chapter 5, Problem 32P

Figure 5-39 shows an overhead view of a 0.0250 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force ${\stackrel{\to }{F}}_1$ has a magnitude of 6.00 N and is at θ₁ = 30.0°. Force ${\stackrel{\to }{F}}_2$ has a magnitude of 7.00 N and is at θ₂ = 30.0°. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity $\stackrel{\to }{v}=\left(13.0\hat{i} -14.0\hat{j}\right)$ m/s, and (c) has the varying velocity $\stackrel{\to }{v}=\left(13.0t\hat{i} -14.0t\hat{j}\right)$ m/s², where t is time?

Figure 5-39 Problem 32.