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The Second Condition of Equilibrium A net torque, Στ, is analogous to a net force (ΣF) when examining its influence on motion. Στ applies to rotational motion the same way ΣF applies to linear motion. A few important notes about torque: Any torque that would try to cause counterclockwise rotation is considered positive. The exact position of where a force acts now becomes very important. The weight of an object seems to act through its center of mass. The words "balanced" or "equilibrium" or "at rest" imply Στ = 0 To solve Torque problems: 1. Draw a sketch. 2. Label the object with given information. 3. Label the weight of the object as a force at the center of gravity (generally the exact middle of the object). 4. Choose a fulcrum. 5. Show the direction of clockwise motion with an arrow. 6. Write the equation, Στcw = Στccw. 7. Write the sum of the clockwise torques, as F1·r1+ F2·r2 + F3·r3, etc…. 8. Repeat for counterclockwise torques. 9. Substitute in any numbers that you have. 10. Solve for the unknown. Practice Rotational Equilibrium: 1. A weight of 2 N is placed 0.2 m from the pivot of a 0.5-N beam. If the beam is 1- m long and the pivot is in the exact center, where should you place a 1.5 N weight to balance the beam? (answer 0.27 m from pivot) 2. A weight of 2 N is placed 0.2 m from the pivot of a 0.5-N beam. If the beam is 1- m long and the pivot is in the exact center, how much weight should be placed at 0.4 m from the pivot to balance the beam? (answer 1N) 3. A weight of 2 N is placed 0.2 m left of the pivot of a 0.5-N beam. If the beam is 1-m long and the pivot is at the 0.3-m mark, where should you place a 1.5 N weight to balance the beam?( 0.2 m from pivot) The Second Condition of Equilibrium Practice 1 1. Two paramedics rush a 60-kg man, carrying him on a 3.00-kg stretcher held by the ends. Orin holds the left side of the stretcher and Ann holds the right side. The stretcher is 2.60-m long and the man’s center of mass is 1.00-m from Ann. How much force must Orin exert to keep the man horizontal? (HINT: Use Ann as the fulcrum.) (answer: 241 N ) 2. A light horizontal bar with a length of 3.00-m has a pivot at its center. If a 102-kg mass is placed 0.80-m away from the left end of the bar. How far away from the left end should the second, 109-kg mass be placed to be in equilibrium? (answer: 2.15 m from left end ) 3. A mass of 80-kg is placed in the middle of a 5.9 m long tree branch. A second mass of 120-kg is placed at the far end of the branch. (The other end of the branch is attached to the tree.) Where would you have to push up with a 4400 N force in order to have the branch stay in equilibrium?( 2 m ) 4. A meterstick is fixed horizontally at its 100-cm mark. Imagine this meterstick is used as a display for some fruits and vegetables with record-breaking masses. A lemon with a mass of 3.9-kg hangs from the 70-cm mark, and a cucumber with a mass of 9.1-kg hangs from the x cm mark. What is the value of x if the other support pushes up with a 56.0 N force at the other end of the meterstick? ( 0.5 m ) The Second Condition of Equilibrium Practice 2 1. A woman who weighs 500 N is standing on a board that weighs 100 N. The board is supported at each end, and the support force at the left end is 150 N. If the board is 8 m long, how far from the right end is the woman standing? (1.6 m) 2. An 800 N billboard worker stands on a 4 m scaffold weighing 500 N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 550 N in that rope? (2.5 m) 3. A meter stick is supported by a knife edge at the 50 cm mark and has masses of 0.40 and 0.60 kg hanging from the 20 cm and 80 cm marks, respectively. Where should a third mass of 0.30 kg be hung to keep the stick balanced? (30 cm)