• Objects in static equilibrium don’t move.

• Of special interest to civil and mechanical engineers and architects.

• We’ll also learn about elastic (reversible) deformations.

• Plastic deformations are irreversible (like play dough)

Chapter 12: (Static) Equilibrium and Elasticity

Reading assignment: Chapter 13.1-13.3

Homework : (due Wednesday, Oct. 26, 2005):

Problems: 4, 10, 24, 31, 35, 42

Objects in static equilibrium don’t

______ or _______.

Conditions for static equilibrium

Conditions for static equilibrium(For ____________ objects)

1. The net force acting on the particle must be _________.

2. The net torque about any axis acting on the particle must be ______.

3. The _______ and _______ speeds must be zero.

0 F

0

Conditions for static equilibrium(For extended objects)

Is this object in static equilibrium?

A force couple is acting on an object. A ___________ ___________ is a pair of forces of equal magnitude and opposite direction along parallel lines of action

It matters at which point the force is applied!!

If equal and opposite forces are applied at the same ___________ or along the same _______________ object is in equilibrium

If equal and opposite forces are applied at _________________ points object is not in equilibrium, since there is a net torque.

Conditions for static equilibrium(For extended objects)

1. The net force acting on the particle must be zero.

2. The net torque about any axis acting on the particle must be zero.

3. The angular and linear speeds must be zero.

0 F

0

We restrict ourselves to forces in the x-y plane. Thus:

0__ F

0__

0__ F

Center of gravity

Consider an extended object.

- The gravitational force ___ always acts on the center of gravity!

- The center of gravity is equal to the center of _______(Ch. 9.2).

How do we treat the _____________ force?

Examples of rigid objects in static equilibrium

We will only consider objects that are _______________ and in a ________________________ gravitational field.

Balanced rock

For this system to be in static equilibrium, the center of gravity must be directly over the support point.

Why??

Problem-solving hints:

Objects in static equilibrium

1. Draw a _____ __________ diagram.

- Show and label all the _______ forces acting on the object.

- Indicate ____________ the forces are applied.

2. Establish a convenient ______________ system for forces. Then apply condition 1: Net force must equal _________.

3. Establish a convenient ____________ system for torque. Then apply condition 2: Net torque must equal ______________.

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.

Black board example 12.1

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.

Black board example 12.2

HW 9

(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?

Elastic properties of solids

We will consider three types of deformations and define an elastic modulus for each.

1. Change in length. _______________ MODULUS measures the resistance of a solid to a change in its length.

2. Shearing. ______________ MODULUS measures the resistance to shearing.

3. Change in volume. _______________ MODULUS measures the resistance to changes in volume.

Elastic properties of solids

Definitions of stress and strain.

Stress: _________ per unit cross sectional area.

Strain: Measure of the degree of ___________.

Elastic properties of solids

Young’s modulus:

iLLAFY

//

______ tensile_____ tensile

Tension or compression

Stress-strain curve

Elastic properties of solids

Shear modulus:

hxAFS

//

_______shear _______shear

Elastic properties of solids

Bulk modulus:

ii VVP

VVAFB

///

______ volume______ volume

P… pressure

Hydraulic _____________ or stress

Black board example 12.4

A 200 kg load is hung on a wire with a length of 4.00 m, a cross-sectional area of 2.00·10-5 m and a Youngs modulus of 8.00·1010 N/m2.

What is its increase in length (Assume elastic deformation)?