Halliday, Resnick & Walker — Force and Motion–I: Problem 64

Figure 5.39 shows a box of mass \( m_2 = 1.0 \text{ kg} \) on a frictionless plane inclined at angle \( \theta = 30^\circ \). It is connected by a cord of negligible mass to a box of mass \( m_1 = 3.0 \text{ kg} \) on a horizontal frictionless surface. The pulley is frictionless and massless. (a) If the magnitude of horizontal force \( \vec{F} \) is 2.3 N, what is the tension in the connecting cord? (b) What is the largest value the magnitude of \( \vec{F} \) may have without the cord becoming slack?