lecture 24 ch12 f18 static equilibrium problems
TRANSCRIPT
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!
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
Today we are going to discuss:
Chapter 12:
Static Equilibrium: Solving Problems
IN THIS CHAPTER, you will discuss static equilibrium of an object
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
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
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
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
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
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
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
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
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
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
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
Example
0 z
0 xF
Beam stability
0 yF
The forces are nonconcurrent, so we need all equilibrium
conditions
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
Find the tension in the two wires supporting the traffic light
Example Traffic light
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
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
The forces are nonconcurrent, so we need all equilibrium
conditions
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
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
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture24A.Danylov
Thank you