Examples on Equilibrium in Physics
Solve physics problems related to equilibrium, including calculating tensions in cables, analyzing forces on pulleys, determining reactions at fixed support points, and finding forces required to maintain weight positions. Detailed solutions and diagrams provided for each problem.
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Problem-1 Calculate the tension T in the cable which supports the 500-kg mass with the pulley arrangement shown. Each pulley is free to rotate about its bearing, and the weights of all parts are small compared with the load. Find the magnitude of the total force on the bearing of pulley C. 9/24/2024 2
Solution Pulley M A : = = = 0 0 T r T r T T 1 2 1 2 O + = + = = 0 = 500 . 9 81 0 2 500 . 9 81 F T T T 1 2 1 y = 2450 N T T 1 2 Pulley = T B = : T = / 2 1226 N T 3 4 2 Pulley C : The T moment T equilibriu = requires m : = or 1226 N T 3 + = = = 0 0 = 1226 cos + 30 0 1062 N F F F x x x + = = 0 0 1226 sin 30 1226 0 613 N F F F y y y = + = + = 2 2 2 2 1062 613 1226 N F F F x y 9/24/2024 3
Problem-2 A cantilever beam OABC is subjected to the forces and moment as shown. (i) Draw free body diagram of the cantilever beam OABC. (ii) Compute the reactions at the fixed support point O. Assume beam is weightless and its thickness is negligible compared to other dimensions. Note the two pulleys, shown in the figure, are smooth. y 300 15 kN.m 1.4 kN 3 kN C O B A x 1.2 m 1.8 m 1.8 m 9/24/2024 4
Solution (i) Free body diagram of the cantilever beam (ii) Reactions at the fixed support O + = + = 5 . 1 = ( ) 0 3 sin 30 0 kN F O O x x x + = 4 . 1 + + = = ) 0 3 cos 30 0 . 3 99 kN F O O y y y + = 4 . 1 + 2 . 1 + + 8 . 4 = = ( ) 0 15 3 cos 30 0 29 kNm 15 . CCW M M M o O O September 24, 2024 5
Problem-3 Determine the force P required to maintain the 200 kg weight in the position. The diameter of the pulley at B is negligible. Given, = 300 . 9/24/2024 6
Solution ( ) 2 2 cos 30 = = tan 15 2 sin 30 + = = 180 30 ( 90 ) 60 T 150 P 600 200 9.81 Free Body Diagram + = + = = 0 sin 60 sin 15 0 3 . 0 = F T P T P x + = + 0 cos 60 cos 15 200 . 9 81 0 F T P y + = T = 3 . 0 = T cos P 60 = cos 15 200 . 9 81 0 = 1758 2 . N P P P = 0 3 . 0.3 1758 2 . 527 5 . N 527 5 . N 9/24/2024 7
Problem-4 The uniform concrete slab shown in edge view has a mass of 25000 kg and is being hoisted slowly into a vertical position by the tension P in the hoisting cable. For the position where = 600 calculate the force T in the horizontal anchor cable. Assume support A is a roller. 9/24/2024 8
Solution Free Body Diagram of Slab . 9 25000 81 2 = = 163500 N P ( ) cos 30 6 sin 60 sin 30 3 = = = cos 30 163500 cos 30 141595 1 . T P = 141 6 . kN T + = = = 0 cos 30 0 cos 30 F T P T P x + = ( ) 0 cos 30 6 sin 60 = CCW M P A . 9 sin 30 3 25000 81 2 0 P 9/24/2024 9
Sample Problem 5 A fixed crane has a mass of 1000 kg and is used to lift a 2400 kg crate. It is held in place by a pin at A and a rocker at B. The center of gravity of the crane is located at G. Determine the components of the reactions at A and B.
Sample Problem 5-Continued y Determine the reaction at B by solving the equation for the sum of the moments of all forces about A. ( 5 . 1 B ) ( ) ( ) 0 = : 0 = + . 9 m 81 kN 2 m 23 5 . kN 6 m MA x = 107 + 1 . kN B Determine the reactions at A by solving the equations for the sum of all horizontal forces and all vertical forces. : 0 = + = B A F x x kN 1 . 107 = x A Draw the free-body diagram 0 = = 0 : . 9 81 kN 23 5 . kN 0 F A y = y + 33 3 . kN A y
Sample Problem 6 The frame supports part of the roof of a small building. The tension in the cable is 150 kN. Determine the reaction forces at the fixed end E.
Sample Problem 6-Continued Solve 3 equilibrium equations for the reaction force components and couple. 5 . 4 : 0 + = x x E F ( ) = 150 kN 0 5 . 7 = 90 kN E x 6 ( ) ( ) = = 0 : 4 20 kN 150 kN 0 F E y y 5 . 7 = 200 + kN E y ( ( 6 . 3 ) ) ( ( 8 . 1 ) ) = : 0 + + Draw a free-body diagram for the frame and the cable. 20 kN 7.2 m 20 kN 4 . 5 m M E + + 20 kN m 20 kN m 6 ( ) 5 . 4 + = 150 kN m 0 M E 5 . 7 m = 180 kN M E
