1. jw Physics 2111 Understanding Physics Chapter 12 1 Fundamentals of Physics Chapter 12 Equilibrium & Elasticity 1.Equilibrium 2.The Requirements of Equilibrium 3.The Center of Gravity 4.Some Examples of Static Equilibrium Problem Solving Tactics 5.Indeterminate Structures 6.Elasticity Tension & Compression Shearing Hydraulic Stress Review & Summary Questions Exercises & Problems

2. jw Physics 2111 Understanding Physics Chapter 12 2 Equilibrium Equilibrium: P and L are constant. Static Equilibrium: Stable Static Equilibrium: body returns to static equilibrium after being displaced by a force. Unstable Equilibrium: a “small” force can displace the body and end the equilibrium,

3. jw Physics 2111 Understanding Physics Chapter 12 3 Requirements of Equilibrium Requirements for Equilibrium: The vector sum of all the external forces that act on the body must be zero. The vector sum of all the external torques that act on the body, measured about any possible point, must be zero. Simplification in Chapter 12: forces are in the xy-plane (torques in z-direction) Newton’s 2 nd Law: vector equations

4. jw Physics 2111 Understanding Physics Chapter 12 4 Center of Gravity The gravitational force F g on a body effectively acts at a stable point, called the Center of Gravity of the body. If g is the same for all parts of a body, then the body’s Center of Gravity is coincident with the body’s Center of Mass.

5. jw Physics 2111 Understanding Physics Chapter 12 5 Equilibrium Stable Equilibrium Neutral Equilibrium

6. jw Physics 2111 Understanding Physics Chapter 12 6 Equilibrium & Center of Gravity cog over the base of support cog beyond the base of support

7. jw Physics 2111 Understanding Physics Chapter 12 7 Problem Solving: Draw a picture relevant to the problem. Choose the system: e.g. “the ladder & man” Draw the corresponding free-body diagram for the system. –Forces –Distances Choose coordinate axes. –Component Force Equations along axes. –Torque Equations (Choose the axis). Algebraically solve the equations. –Solve for the unknowns. –Check that units are correct. Plug in the numbers. Set significant figures for the answer(s).

8. jw Physics 2111 Understanding Physics Chapter 12 8 What are the forces on the ladder from the wall and pavement? half-way up ladder frictionless wall L = 12 m M L = 45 kg h = 9.3 m com = L/3 from bottom M F = 72 kg climbs halfway up Forces on ladder from wall, pavement

9. jw Physics 2111 Understanding Physics Chapter 12 9 Fireman on the Ladder Choose rotation axis here h

10. jw Physics 2111 Understanding Physics Chapter 12 10 Elasticity A rigid body is a 3D matrix of atoms (or molecules) held together by inter-atomic forces. All rigid bodies are elastic - deform under stress. Stress = “Modulus of Elasticity” X Strain Force  Stress  Deformation  Strain

11. jw Physics 2111 Understanding Physics Chapter 12 11 Elasticity Apply a stretching force to a bar: This force gets distributed over the surface area of the bar: Force per unit area is defined as the stress.

12. jw Physics 2111 Understanding Physics Chapter 12 12 Elasticity If this sample bar is pulled on, what happens?

13. jw Physics 2111 Understanding Physics Chapter 12 13 Elasticity Tension & Compression Shearing Hydraulic Stress Young’s Modulus (aka Y) Shear Modulus Bulk Modulus

14. jw Physics 2111 Understanding Physics Chapter 12 14 tension in rope & normal force from wall? Equilibrium: vector equation

15. jw Physics 2111 Understanding Physics Chapter 12 15 forces on the 4 tires of a car? L L cog Vertical forces: car Torque about rear axle:

16. jw Physics 2111 Understanding Physics Chapter 12 16 Example: biceps lifts a weight; force on elbow?

17. jw Physics 2111 Understanding Physics Chapter 12 17 Example: biceps lifts a weight; force on elbow?

18. jw Physics 2111 Understanding Physics Chapter 12 18 FNFN FeFe mg Example: force to raise the wheel over the edge? Forces on the wheel

19. jw Physics 2111 Understanding Physics Chapter 12 19 T = ? Force on Hinge = ? mg Mg T FXFX FYFY M m m strut =25kg

20. jw Physics 2111 Understanding Physics Chapter 12 20 nut cracks @ 40 N on both sides; Torques about hinge: “Mechanical Advantage”:

21. jw Physics 2111 Understanding Physics Chapter 12 21 Suspended Blocks