13.3: Normal and Tangential Components: Problem Solving
Consider a man with a mass of 70 kg seated in a chair connected to a pin support through a member BC. If the man maintains an upright position, the task is to determine the horizontal and vertical reactions of the chair on the man when the member makes a 45° angle with the horizontal. At this moment, the man has a speed of 5 m/s, increasing at a rate of 1 m/s².
As the man moves along a curvilinear path, the tangential acceleration is given as 1 m/s². The normal acceleration can be calculated using the tangential speed and the curvature radius. A free-body diagram of the man is then drawn, and the equations of motion for tangential and normal components are formulated.
Two equations are derived by substituting known values and assuming the acceleration due to gravity as 10 m/s², revealing the required reaction forces. Solving these equations simultaneously provides the magnitudes of the reaction forces along the horizontal and vertical directions.
This analytical approach offers a systematic method for determining the chair's reactions on the man under specific conditions, considering the dynamic aspects of the man's motion and acceleration.
