Understanding Equilibrium in Rigid Bodies
Explore the concept of equilibrium in rigid bodies through problem-solving scenarios involving forces, moments, and tensions. Learn how to ensure balance and stability in resting bodies by analyzing forces and moments. Diagrams and step-by-step calculations help in understanding the physics behind equilibrium in rigid bodies in various positions.
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Statics of rigid bodies You need to be able to solve problems about rigid bodies that are resting in equilibrium If a body is resting in equilibrium: There is no resultant force in any direction, so the horizontal and vertical forces sum to 0 The sum of moments about any point is 0 (the point does not have to be on the body itself) 5B
Statics of rigid bodies D You need to be able to solve problems about rigid bodies that are resting in equilibrium TCos40 T (2) V 40 TSin40 40 A B 3m H C 1m 2m A uniform rod AB, of mass 6kg and length 4m, is smoothly hinged at A. A light inextensible string is attached to the rod at a point C where AC = 3m, and the point D, which is vertically above point A. If the string is keeping the rod in equilibrium in a horizontal position and the angle between the string and the rod is 40 , calculate: (1) 6g Start with a diagram and label on all the forces split the tension into horizontal and vertical components At the hinge there will be a vertical reaction and a horizontal reaction Take moments about point A (as we have 3 unknown forces, 2 will be eliminated by doing this!) (1) 6? 2 = 12? ?? ????????? (2) ????40 3 = 3????40 ?? ????????????? a) The tension in the string ? = 61? These must be equal as the rod is in equilibrium 3????40 = 12? b) The magnitude and direction of the reaction at the hinge. Divide by 3Sin40 12? 3???40 ? = Calculate ? = 61? 5B
Statics of rigid bodies D You need to be able to solve problems about rigid bodies that are resting in equilibrium 61Cos40 61 V 40 61Sin40 40 A B 3m H C 1m A uniform rod AB, of mass 6kg and length 4m, is smoothly hinged at A. A light inextensible string is attached to the rod at a point C where AC = 3m, and the point D, which is vertically above point A. If the string is keeping the rod in equilibrium in a horizontal position and the angle between the string and the rod is 40 , calculate: 6g Resolve Horizontally (set left and right forces equal to each other) ? = 61???40 Calculate ? = 46.72? Resolve Vertically (set upwards and downwards forces equal to each other) a) The tension in the string ? = 61? ? + 61???40 = 6? Subtract 61Sin40 b) The magnitude and direction of the reaction at the hinge. ? = 6? 61???40 Calculate ? = 46.72? ? = 19.6? ? = 19.6? 5B
Statics of rigid bodies D You need to be able to solve problems about rigid bodies that are resting in equilibrium 61Cos40 61 V 40 61Sin40 40 A B 3m H C 1m A uniform rod AB, of mass 6kg and length 4m, is smoothly hinged at A. A light inextensible string is attached to the rod at a point C where AC = 3m, and the point D, which is vertically above point A. If the string is keeping the rod in equilibrium in a horizontal position and the angle between the string and the rod is 40 , calculate: 6g R R V V 19.6 A A a) The tension in the string ? = 61? H 46.72 H The resultant force will be somewhere between V and H Use a right-angled triangle to help b) The magnitude and direction of the reaction at the hinge. 46.722+ 19.62 ????????? = ? = 46.72? ? = 19.6? Calculate ????????? = 50.6? ????????? = 50.6? 5B
Statics of rigid bodies D You need to be able to solve problems about rigid bodies that are resting in equilibrium 61Cos40 61 V 40 61Sin40 40 A B 3m H C 1m A uniform rod AB, of mass 6kg and length 4m, is smoothly hinged at A. A light inextensible string is attached to the rod at a point C where AC = 3m, and the point D, which is vertically above point A. If the string is keeping the rod in equilibrium in a horizontal position and the angle between the string and the rod is 40 , calculate: 6g R R V V 19.6 A A a) The tension in the string ? = 61? H 46.72 H You also need to calculate the angle above the horizontal b) The magnitude and direction of the reaction at the hinge. 19.6 46.72 ????? = ??? 1 ? = 46.72? ? = 19.6? Calculate ????????? = 50.6? ,22.8 ????? ? ? ????????? ????? = 22.8 5B
