Walker, Halliday & Resnick — Force and Motion-II: Problem 32

32 A block is pushed across a floor by a constant force \(\vec{F}\) that is applied at downward angle \(\theta\) (Fig. 6-17). Figure 6-38 gives the acceleration magnitude \(a\) versus a range of values for the coefficient of kinetic friction \(\mu_k\) between block and floor: \(a_1 = 3.0 \text{ m/s}^2\), \(\mu_{k2} = 0.20\), and \(\mu_{k3} = 0.40\). What is the value of \(\theta\)?