2. Static Equilibrium A common misconception about equilibrium is that an object is not moving. BUT, as you saw from our definition of equilibrium on page 1, an object can be moving and still be in equilibrium. For example, a hild on a slide sliding down at a constant speed is in mechanical equilibrium. A bike tire being uspended but rotated is also in equilibrium. If we want to define an equilibrium where there is no motion ind no rotation, then we need to add to our previous definition. rigid body is in static equilibrium if two conditions are satisfied: 1. EF = 0 ii. E7 =0 As you can see, we need to impose that the sum of the torques on the object are also zero. This ensures here is no translational motion and rotational motion. Luckily for us, the addition of this constraint doesn't alter our problem-solving steps: 1. Draw a Free Body diagram . This is crucial! No matter how complicated the problem seems, it can always be made simpler with a good, simple free body diagram 2. Establish a coordinate system 3. Establish an axis of rotation . This is important for the torque part 4. Set up your equations following from E F = 0 . [Fx = 0 and EFy = 0 5. Set up your equations following from Ef = 0 . Etcw = Etcew What determines if a torque is CW or CCW depends on where the axis of rotation is! Problem 1 The figure to the right shows a construction worker standing on a uniform beam. The beam has a mass of 85 kg and a length of L = 20 m. The construction work in the figure has a mass of 1 10 kg and is standing 5 m from the hinge (black dot). A cable (assume it's massless) is connected from the wall to the end of the beam and makes and angle of 0 = 30% (15 pts) a) Draw a free body diagram for the beam. Include all forces acting on the beam (you should have 5 force vectors) b) Put the axis of rotation at the hinge. Which forces produce a torque about the hinge? Which forces do not? c) Write out the equation for equilibrium (equations (i) and (ii) on page 6) L d) Solve for the tension in the cableProblem 2 A 66 kg diver stands at the end of a 3 m diving board as shown below. The diving board has a uniform mass of 25 kg. The board is attached to a hinge (black dot) at the left end and rests on top of the right support. (15 pts) 1.5 m a) Draw a free body diagram for the beam. Include all forces acting on the beam (you should have 4 force vectors) b) Put the axis of rotation at the hinge. Which forces 3.0 m produce a torque about the hinge? Which forces do not? Write out the equation for equilibrium (equations (i) and (ii) on page 6) d) Solve for the vertical force exerted by the hinge and by the right support Problem 3 A bowler holds a bowling ball (M = 7.3 kg) in the palm of their hand as shown. The mass of forearm is 2 Bleeps kg. (20 pts) a) Draw a free body diagram for the forearm. Elbow Include all forces acting on the forearm (you contact point should have 4 force vectors) -4.0 cm Lower arm -15 cm (forearm plus b) Put the axis of rotation at the elbow contact -35 cm hand) center point. Which forces produce a torque about of mass the elbow? Which forces do not? c) Write out the equation for equilibrium (equations (i) and (ii) on page 6) d) What is the magnitude of the force of the biceps muscle on the forearm? e) What is the magnitude of the force of the biceps muscle if the forearm is lowered 30"? If the maximum force the biceps can handle is 1000 N, what's the heaviest weight you can hold if the forearm is in the horizontal position