Chapter 9

Static Equilibrium

Conditions for Equilibrium

• What are the conditions for equilibrium?

What if…

• We look at a book sitting on a table

• Is it moving?

Equilibrium

• The book is experiencing forces but is not moving

• It is in equilibrium

• Latin for equal forces

Braces• The wire band

around the teeth has a tension TF of 2.0 N along it. What is the resultant force on the highlighted tooth?

• Draw a force diagram of the tooth.

Braces• The wire band exerts

the FT in each direction along the wire.

• Since the forces are equal and in opposite directions, the FR will be along the line that bisects the angle between them.

Braces

• Call the direction of FR the y axis

• What will be the sum of the forces in the x direction?

• What will be the sum of forces in the y direction (FR)?

• Result of this?

Equilibrium

• Was the tooth in equilibrium?

• First condition of equilibrium:

• Must be zero along each axis (including z!)

Chandelier

• Calculate the tension FA and FB in the two cords that are connected to the vertical cord supporting the 200 kg chandelier.

• Draw a free-body diagram of what?

Chandelier

• Pick the point where the three cords meet

• Sum in the forces in the x and y direction

• Resolve FA into components

Equilibrium

Equilibrium?

Equilibrium

• The forces add up to zero, but…

• The forces produce a net torque that will rotate the object

• Couple: A pair of equal forces acting in opposite directions but at different point in on object

Equilibrium

• Second condition for equilibrium:

• The sum of the torques must be zero

Lever

• A bar is placed over a small rock to act as a lever on the large rock

• The lever should allow a smaller FP

• What if FP is still not large enough?

Mechanical Advantage

• Torque of FP must be equal or greater than mg so we can say

• mgr = FPR

• Rearrange

• Define Mechanical Advantage as r/R

Homework

• Read Section 9.1