lecture 24 ch12 f18 static equilibrium problems

DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov

Lecture 24

Chapter 12

Static Equilibrium.Solving Problems.

Physics I

The end of the semester!

Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-i/

Thank you!


Today we are going to discuss:

Chapter 12:

Static Equilibrium: Solving Problems

IN THIS CHAPTER, you will discuss static equilibrium of an object


Precession of a Bicycle WheelGyroscope (section 12.12 “for fun” )

x

y

zmg

rAxisofrotation

Rot.N2nd Law

Whatisadirectionoftorque?

A)Along+xB)Along‐xC)Along+y

E)Along+zD)Along‐y


Static Equilibrium

0)1 xF 0)2 yF 0)3 z

There are three resulting equations, which we will use

The choice of an axis is arbitrary


Concurrent/Nonconcurrent forces

1F 2F

3F

Concurrent forces:when the lines of action of the forces intersect at a common point, there will be no rotation. So

1F 2F

3F

0 xF 0 yF0 z 0 xF 0 yF0 z

Nonconcurrent forces:when the lines of action of the forces do not intersect at a common point, there will be rotation. So

Automatically satisfied


Recall how to calculate torque (shortcut)

Fr

F

r

• Draw a line of force • Find the perpend. distance (r┴) from

the axis of rotation to that line.• Magnitude of torque is r┴F• Torque is positive if it tries to rotate an

object CCW

sinrF

Line of force (action)

r Fr

Lecture 20


Example

0 z

0 xF

A ladder of length l and mass Mleans against a frictionless wall andit makes an angle θ with the floor.A man of mass m climbs slowly upthe ladder and when he is at adistance d from the base of theladder, the ladder is about to startsliding. Calculate the coefficient ofstatic friction between the ladderand the floor.

Ladder stability with a guy

0 yF

The forces are nonconcurrent, so we need all equilibrium

conditions


Example

0 z

0 xF

Beam stability

0 yF


conditions


Find the tension in the two wires supporting the traffic light

Example Traffic light


Example

0 z

0 xF

A 3.0-m-long ladder leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.40. What is the minimum angle the ladder can make with the floor without slipping?

Ladder stability (12.58)

0 yF


conditions


1. Choose one object at a time, and make a free-body diagram by showing all the forces on it and where they act.

2. Choose a coordinate system and resolve forces into components.

3. Write equilibrium equations for the forces.

4. Choose any axis perpendicular to the plane of the forces and write the torqueequilibrium equation. A clever choice here can simplify the problem enormously.

5. Solve.

Solving Statics Problems


Thank you

lecture 24 ch12 f18 static equilibrium problems

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