Fundamentals of Physics

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

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, Physics 2111 Understanding Physics

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. Newton’s 2nd Law: vector equations Simplification in Chapter 12: forces are in the xy-plane (torques in z-direction) Physics 2111 Understanding Physics

4. Center of Gravity The gravitational force Fg 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. Physics 2111 Understanding Physics

5. Equilibrium Neutral Equilibrium Stable Equilibrium Physics 2111 Understanding Physics

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

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). Physics 2111 Understanding Physics

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

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

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. Force  Stress  Deformation  Strain Stress = “Modulus of Elasticity” X Strain Physics 2111 Understanding Physics

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

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

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

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

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

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

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

18. Example: force to raise the wheel over the edge? Forces on the wheel mg Fe FN Physics 2111 Understanding Physics

19. T FY FX T = ? Force on Hinge = ? mstrut=25kg Mg m M mg Physics 2111 Understanding Physics

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

21. Suspended Blocks Physics 2111 Understanding Physics