Solved: A uniform ball of weight 50 lb is supported by two frictionless planes as shown

Chapter 7, Problem 48

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A uniform ball of weight 50 lb is supported by two frictionless planes as shown in FIGURE 7.R.2. Let the force exerted by the supporting plane \(\mathscr{P}_{1}\) on the ball be \(F_1\) and the force exerted by the plane \(\mathscr{P}_{2}\) be \(F_2\). Since the ball is held in equilibrium, we must have \(w+F_1+F_2=0\), where w = -50j. Find the magnitudes of the forces \(F_1\) and \(F_2\). [Hint: Assume the forces \(F_1\) and \(F_2\) are normal to the plane \(\mathscr{P}_{1}\) and \(\mathscr{P}_{2}\), respectively, and act along lines through the center C of the ball. Place the origin of a two-dimensional coordinate system at C.]