chapter 12 static equilibrium. equilibrium we already introduced the concept of equilibrium in...
DESCRIPTION
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 bodyTRANSCRIPT
Chapter 12
Static Equilibrium
Equilibrium
• We already introduced the concept of equilibrium in Chapter 7: dU(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
constLconstP
;
0;0 LP
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
0;0 LP
Equilibrium
• Stable equilibrium:
• Unstable equilibrium:
02
2
dx
Ud
02
2
dx
Ud
Chapter 12Problem 25
A particle’s potential energy as a function of position is given by U = 2x3 – 2x2 – 7x + 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
0 ; netFdtPdconstP
0 ; netdtLdconstL
Equilibrium: 2D case
• If an object can move only in 2D (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)
0;0 ,, ynetxnet FF
0, znet
Examples of static equilibrium
Examples of static equilibrium
Chapter 12Problem 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 overhangthe desk