Serway & Jewett — The Laws of Motion: Problem 40

A 1.00-kg glider on a horizontal air track is pulled by a string at an angle \(\theta\). The taut string runs over a pulley and is attached to a hanging object of mass 0.500 kg as shown in Figure P5.40. (a) Show that the speed \(v_x\) of the glider and the speed \(v_y\) of the hanging object are related by \(v_x = uv_y\), where \(u = z(z^2 - h_0^2)^{-1/2}\). (b) The glider is released from rest. Show that at that instant the acceleration \(a_x\) of the glider and the acceleration \(a_y\) of the hanging object are related by \(a_x = ua_y\). (c) Find the tension in the string at the instant the glider is released for \(h_0 = 80.0 \text{ cm}\) and \(\theta = 30.0^\circ\).