Unformatted text preview: Chapter 9
Static Equilibrium Statics and Equilibrium Equilibrium when the net force and the net torque acting on an object is zero. Object is either at rest or in motion at a constant velocity. Statics study of the forces acting on and within objects in equilibrium. Types of Equilibrium Stable Equilibrium once displaced the object returns to its original position. Unstable Equilibrium once displaced the object loses its equilibrium and accelerates away from its original position. Neutral Equilibrium once displace the object remains stationary in a new equilibrium position Types of Equilibrium
Example: What type of equilibrium exists for the ball in each of the three locations below? 1st Condition of Equilibrium sum of all the forces acting on an object must be equal to zero. Conditions of Equilibrium
Fy=0 Fz=0 2nd Condition of Equilibrium the sum of all the torques acting on an object must be equal to zero.
=0 In order to calculate the torques an arbitrary axis of rotation must be chosen. ANY point may be taken to be the axis since the object will not rotate if in equilibrium. Chose a point that makes the problem easiest. Fx=0 Problem Solving with Statics Step 1: Draw a FBD (chose an xy plane, resolve forces in to x and y components) Step 2: If an extended object, chose an axis of rotation, usually one that eliminates a torque or one for which torque arms are easily measured. Step 3: Apply the equilibrium equations for forces and torque. Step 4: Solve for unknowns. You may need multiple equations for multiple unknowns. Problem Solving with Statics Example: Find the tension in the two ropes. Example: How far from the pivot point on a seesaw must an 80 kg man sit to exactly balance a 150 kg man sitting 2 meters from the pivot point on the opposite side? (Ignore the mass of the seesaw) Problem Solving with Statics Example: A 50.0 N weight is held in a person's hand with the forearm horizontal as shown. The biceps muscle is attached 0.03 m from the joint and the weight is 0.35 m from the joint. Calculate the upward force exerted by the biceps muscle and the downward force exerted by the humerus bone. Problem Solving with Statics Example: A uniform section of a bridge is 80 m long with a mass of 12000 kg and is supported at either end. A 1000 kg car sits 10 meters from one end of the section. What is the force in exerted by each support? Problem Solving with Statics A 700 N bear walks out along a uniform beam that is 6.00 m long and weighs 200 N toward a basket of goodies that weigh 80 N. The end of the beam is supported by a wire that makes and angle of 60.0 degrees. If the maximum tension the wire can withstand is 900 N, can the bear reach the goodies? ...
View Full Document