Problem 3. The truck with a ladder plotted in Fig. 3 starts from rest (and accelerates...

Transcribed Image Text:

Problem 3. The truck with a ladder plotted in Fig. 3 starts from rest (and accelerates to the left) with an acceleration of 7 m/s. The ladder of mass m = 10 kg, which is the rigid body of interest in this problem, can be modeled as a uniform slender rod that is hinged at point A and supported at point B. As a consequence, the center of mass G of the ladder is located at the midpoint of the rod. Any friction in this problem is supposed to be small enough to be neglected. a) Determine the minimum linear acceleration amin of the truck such that the ladder loses contact at point B, i.e. the normal force N at B vanishes, and starts to rotate about point A. Do so by determining the sum of the moments about point A, and verify that for the given acceleration of the truck, the ladder will in fact lose contact at point B. b) Determine the mass moment of inertia of the ladder associated with its center of mass G. c) Use the result found in Part b) and employ the concept of relative acceleration expressed in terms of a normal-tangential coordinate system to determine the initial angular acceleration vector o of the ladder. 1.5m 2m Figure 3: A truck with a ladder accelerating from rest to the left and measurements. Problem 3. The truck with a ladder plotted in Fig. 3 starts from rest (and accelerates to the left) with an acceleration of 7 m/s. The ladder of mass m = 10 kg, which is the rigid body of interest in this problem, can be modeled as a uniform slender rod that is hinged at point A and supported at point B. As a consequence, the center of mass G of the ladder is located at the midpoint of the rod. Any friction in this problem is supposed to be small enough to be neglected. a) Determine the minimum linear acceleration amin of the truck such that the ladder loses contact at point B, i.e. the normal force N at B vanishes, and starts to rotate about point A. Do so by determining the sum of the moments about point A, and verify that for the given acceleration of the truck, the ladder will in fact lose contact at point B. b) Determine the mass moment of inertia of the ladder associated with its center of mass G. c) Use the result found in Part b) and employ the concept of relative acceleration expressed in terms of a normal-tangential coordinate system to determine the initial angular acceleration vector o of the ladder. 1.5m 2m Figure 3: A truck with a ladder accelerating from rest to the left and measurements.