Chapter 12 Static Equilibrium Equilibrium We already introduced

Chapter 12 Static Equilibrium

Equilibrium • We already introduced the concept of equilibrium in Chapter 7: d. U(x)/dx = 0 • More general definition of equilibrium: • Static equilibrium: • Stable equilibrium: the body returns to the state of static equilibrium after having been displaced from that state. Unstable equilibrium: the state of equilibrium is lost after a small force displaces the body

Equilibrium • Static equilibrium: • Stable equilibrium: the body returns to the state of static equilibrium after having been displaced from that state. Unstable equilibrium: the state of equilibrium is lost after a small force displaces the body

Equilibrium • Stable equilibrium: • Unstable equilibrium:

Chapter 12 Problem 25 A particle’s potential energy as a function of position is given by U = 2 x 3 – 2 x 2 – 7 x + 10, with x in meters and U in joules. Find the positions of any stable and unstable equilibria.

Center of mass: stable equilibrium • We consider the torque created by the gravity force (applied to the CM) and its direction relative to the possible point(s) of rotation

Center of mass: stable equilibrium • We consider the torque created by the gravity force (applied to the CM) and its direction relative to the possible point(s) of rotation

Center of mass: stable equilibrium • We consider the torque created by the gravity force (applied to the CM) and its direction relative to the possible point(s) of rotation

Center of mass: stable equilibrium • We consider the torque created by the gravity force (applied to the CM) and its direction relative to the possible point(s) of rotation

The requirements of equilibrium • For an object to be in equilibrium, we should have two requirements met • Balance of forces: the vector sum of all the external forces that act on the body is zero • Balance of torques: the vector sum of all the external torques that act on the body, measured about any possible point, is zero

Equilibrium: 2 D case • If an object can move only in 2 D (xy plane) then the equilibrium requirements are simplified: • Balance of forces: only the x- and y-components are considered • Balance of torques: only the z-component is considered (the only one perpendicular to the xy plane)

Examples of static equilibrium

Examples of static equilibrium

Chapter 12 Problem 38 A crane in a marble quarry is mounted on the quarry’s rock walls and is supporting a 2500 -kg marble slab as shown in the figure. The center of mass of the 830 -kg boom is located one-third of the way from the pivot end of its 15 -m length, as shown. Find the tension in the horizontal cable that supports the boom.

Indeterminate structures • Indeterminate systems cannot be solved by a simple application of the equilibrium conditions • In reality, physical objects are not absolutely rigid bodies • Concept of elasticity is employed

Questions?

Answers to the even-numbered problems Chapter 12 Problem 24: (a) 47 m from the origin (b) unstable

Answers to the even-numbered problems Chapter 12 Problem 36: 1. 2 m

Answers to the even-numbered problems Chapter 12 Problem 54: L/6 of the bottom book can overhang the desk