1 Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli Piri Reis University / Physics -I

2 Piri Reis University Fall Semester Physics -I Chapter 12 Static Equilibrium; Elasticity and Fracture

3 Piri Reis University Lecture XII I. The Conditions for Equilibrium II. Solving Statics Problems III. Applications to Muscles and Joints IV. Stability and Balance V. Elasticity; Stress and Strain VI. Fracture VII. Spanning a Space: Arches and Domes

4 I. The Conditions for Equilibrium An object with forces acting on it, but that is not moving, is said to be in equilibrium.

5 I. The Conditions for Equilibrium The first condition for equilibrium is that the forces along each coordinate axis add to zero.

6 I. The Conditions for Equilibrium The second condition of equilibrium is that there be no torque around any axis; the choice of axis is arbitrary.

7 II. Solving Statics Problems 1. Choose one object at a time, and make a free-body diagram showing all the forces on it and where they act. 2. Choose a coordinate system and resolve forces into components. 3. Write equilibrium equations for the forces. 4. Choose any axis perpendicular to the plane of the forces and write the torque equilibrium equation. A clever choice here can simplify the problem enormously. 5. Solve.

8 II. Solving Statics Problems The previous technique may not fully solve all statics problems, but it is a good starting point.

9 II. Solving Statics Problems If a force in your solution comes out negative (as F A will here), it just means that it’s in the opposite direction from the one you chose. This is trivial to fix, so don’t worry about getting all the signs of the forces right before you start solving.

10 II. Solving Statics Problems If there is a cable or cord in the problem, it can support forces only along its length. Forces perpendicular to that would cause it to bend.

11 III. Applications to Muscles and Joints These same principles can be used to understand forces within the body.

12 III. Applications to Muscles and Joints The angle at which this man’s back is bent places an enormous force on the disks at the base of his spine, as the lever arm for F M is so small.

13 IV. Stability and Balance If the forces on an object are such that they tend to return it to its equilibrium position, it is said to be in stable equilibrium.

14 IV. Stability and Balance If, however, the forces tend to move it away from its equilibrium point, it is said to be in unstable equilibrium.

15 IV. Stability and Balance An object in stable equilibrium may become unstable if it is tipped so that its center of gravity is outside the pivot point. Of course, it will be stable again once it lands!

16 IV. Stability and Balance People carrying heavy loads automatically adjust their posture so their center of mass is over their feet. This can lead to injury if the contortion is too great.

17 A uniform 40.0 N board supports a father (800 N) and daughter (350 N) as shown. The support is under the center of gravity of the board and the father is 1.00 m from the center. (a)Determine the magnitude of the upward force n exerted on the board by the support. (b)Determine where the child should sit to balance the system. Example 1

18 A diver of weight 580 N stands at the end of a 4.5 m diving board of negligible mass (see Fig). The board is attached to two pedestals 1.5 m apart. Example 2 (a)Draw a free body diagram. (b)What are the magnitude and direction of the force on the board from left pedestal? (c)What are the magnitude and direction of the force on the board from right pedestal? (d)Which pedestal is being stretched and which is compressed?

19 V. Elasticity; Stress and Strain Hooke’s law: the change in length is proportional to the applied force.

20 V. Elasticity; Stress and Strain This proportionality holds until the force reaches the proportional limit. Beyond that, the object will still return to its original shape up to the elastic limit. Beyond the elastic limit, the material is permanently deformed, and it breaks at the breaking point.

21 V. Elasticity; Stress and Strain The change in length of a stretched object depends not only on the applied force, but also on its length and cross-sectional area, and the material from which it is made. The material factor is called Young’s modulus, and it has been measured for many materials. The Young’s modulus is then the stress divided by the strain.

22 V. Elasticity; Stress and Strain In tensile stress, forces tend to stretch the object.

23 Elastic properties of solids Young’s modulus: Tension or compression

24 Elastic properties of solids Shear modulus:

25 Elastic properties of solids Bulk modulus: Hydraulic stress

26 HOMEWORK Giancoli, Chapter 12 10, 11, 13, 20, 23, 27, 29, 32, 57, 59 References o “Physics For Scientists &Engineers with Modern Physics” Giancoli 4 th edition, Pearson International Edition