Term: Sum 25 Lesson: 01
Subject: ARCE 302 – WORK AND ENERGY
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GOALS
1
WORK and ENERGY
2
REVIEW/REMINDER
SECTION 8.2 and 8.2
o EQUILIBRIUM TO DETERMINE
WORK = FORCE DISTANCE
UNKNOWN FORCES
WORK and ENERGY are closely related
NORMAL (T/C)
ENERGY is the STORE HOUSE to do WORK and
AXIAL
is known as POTENTIAL ENERGY (I am not doing
BENDING
anything, just sitting here, but I do something
SHEAR
IF I MOVE)
DIRECT
Chemical
BENDING
Gravitational
o THERE IS ALSO DISPLACEMENTS
Nuclear
o HOOKS LAW
Mechanical
USE DISPLACEMENT TO DETERMINE
On a SYSTEM this total store of energy CANNOT
UNKNOWN FORCES
change – CONSERVATION of ENERGY
ENERGY METHOD – VIRTUAL WORK
AXIAL MEMBERS (TRUSS)
Overall goal of class is to solve for INDETERMINATE
members, but have to start at beginning.
WORK and ENERGY
3
When MOVEMENT occurs, then SOME of the
STORE of ENERGY CHANGES to KINETIC
ENERGY, but the TOTAL does NOT change.
Thermal (movement of heat)
Sound (movement of waves through a material)
Radiant (electro-magnetic movement of waves,
note it does not need a material to move through,
it can move through a void like space)
Electrical (movement of electrons)
Motion (physical movement)
Tracking the change of the store house of energy
(POTENTIAL) to the MOVEMENT of ENERGY (KINETIC) is
WORK
We will only be working with MOTION (pun intended)
WORK as MOTION only
WORK = FORCE times PHYSICAL MOVEMENT
WE CALL MOVEMENT - A DEGREE of FREEDOM
WHAT ARE THE DoF FOR 2-dimensions
X, Y and ROTATION
X and Y Movement
WORK = F d
MORE IMPORTANTLY IS FORCE HAS TO BE IN THE
DIRECTION OF MOVEMENT, THUS ADD COSINE
WORK = F d cos()
OR we can break up a diagonal movement into
components W = FX δX + FY δY
Note the term MOVE, it will be displacement for us
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Term: Sum 25 Lesson: 01
Subject: ARCE 302 – WORK AND ENERGY
2 of 2
TOTAL WORK
6
WORK as MOTION only
ROTATION MOVEMENT
5
𝑑
The total work = ∫0 𝐹 𝜕𝑑 for distance
𝜗
What is the Force of Rotation? MOMENT
The total work = ∫0 𝑀 𝜕𝜗
What is the distance of Rotation? AN ANGLE
INTEGRATION IS AREA UNDER A CURVE
Work = Moment times Theta eq. 8.2
Overall goal of class is to solve for INDETERMINATE
members, but have to start at beginning.
STRAIN ENERGY
CLOSE INSPECTION OF EQUATIONS
7
𝑑
∫0 𝐹 𝜕𝑑 THIS IS RESPECT TO THE CHANGE IN
DISPLACEMENT NOT THE LENGTH.
REMEMBER WE DO NOT ENGINEER IN
TERMS OF FORCE AND DISPLACEMENT
So, HOW DOES THE STRESS CHANGE WITH
RESPECT TO STRAIN? HOOKES LAW
WHICH LINEAR,
THUS, WE USE THE TRIANGULAR AREA
Overall goal of class is to solve for INDETERMINATE
members, but have to start at beginning.
STRAIN ENERGY
STRAIN EVERGY = U
8
0
