Serway & Jewett — Static Equilibrium and Elasticity: Problem 36

Why is the following situation impossible? A worker in a factory pulls a cabinet across the floor using a rope as shown in Figure P12.36a. The rope makes an angle \(\theta = 37.0^\circ\) with the floor and is tied \(h_1 = 10.0\text{ cm}\) from the bottom of the cabinet. The uniform rectangular cabinet has height \(\ell = 100\text{ cm}\) and width \(w = 60.0\text{ cm}\), and it weighs \(400\text{ N}\). The cabinet slides with constant speed when a force \(F = 300\text{ N}\) is applied through the rope. The worker tires of walking backward. He fastens the rope to a point on the cabinet \(h_2 = 65.0\text{ cm}\) off the floor and lays the rope over his shoulder so that he can walk forward and pull as shown in Figure P12.36b. In this way, the rope again makes an angle \(\theta = 37.0^\circ\) with the horizontal and again has a tension of \(300\text{ N}\). Using this technique, the worker is able to slide the cabinet over a long distance on the floor without tiring.