1. 2.001 - MECHANICS AND MATERIALS I
Lecture #1
9/6/2006
Prof. Carol Livermore
A first course in mechanics for understanding and designing complicated
systems.
PLAN FOR THE DAY:
1. Syllabus
2. Review vectors, forces, and moments
3. Equilibrium
4. Recitation sections
BASIC INGREDIENTS OF 2.001
1. Forces, Moments, and Equilibrium → Statics (No acceleration)
2. Displacements, Deformations, Compatibility (How displacements fit to-
gether)
3. Constitutive Laws: Relationships between forces and deformations
Use 2.001 to predict this problem.
HOW TO SOLVE A PROBLEM
RULES:
1. SI inits only.
2. Good sketches.
• Labeled coordinate system.

2. • Labeled dimensions and forces.
3. Show your thought process.
4. Follow all conventions.
5. Solve everything symbolically until the end.
6. Check answer ⇒ Does it make sense?
• Check trends.
• Check units.
7. Convert to SI, plug in to get answers.
VECTORS, FORCES, AND MOMENTS
Forces are vectors (Magnitude and Direction)
i j ˆ
F = Fxˆ + Fy ˆ + Fz k
OR
∗ ∗ ˆ
F = Fx∗ iˆ + Fy∗ jˆ + Fz∗ k ∗
Where do forces come from?
• Contact with another object
• Gravity
• Attractive of repulsive forces
Moments are vectors. (Moment is another word for torque.)
• Forces at a distance from a point
• Couple

3. Moments are vectors.
M = My ˆ
j.
EX:
2D:
FB = FBxˆ + FBy ˆ
i j
rAB = rABxˆ + rABy ˆ
i j
MA = rAB × FB =
= (rABxˆ + rABy ˆ × (FBxˆ + FBy ˆ
i j) i j)
= (rAB FB − rAB FB )k ˆ
x y y x
OR
MA = |rAB | FB sin φ using Right Hand Rule
3D:
i j ˆ
rAB = rABxˆ + rABy ˆ + rABz k
i j ˆ
FB = FBxˆ + FBy ˆ + FBz k
ˆ
MA = rAB ×FB = (rABx FBy −rABy FBx )k +(rABz FBx −rABx FBz )ˆ
j+(rABy FBz −rABz FBy )ˆ
i
3

4. EX: Wrench
rAB = dˆ
j
FB = FBˆ
i
j i ˆ
MA = rAB × FB = dˆ × FBˆ = −dFB k
Equations of Static Equilibrium
ΣFx = 0
ΣF = 0 ΣFy = 0
ΣFz = 0
ΣM0 x = 0
ΣM0 = 0 ΣM0 y = 0
ΣM0 z = 0

5. 4
F =0
i=1
F1 + F2 + F3 + F4 = 0
F1x + F2x + F3x + F4x = 0
F1y + F2y + F3y + F4y = 0
F1z + F2z + F3z + F4z = 0
Mo = 0
⇒ r01 × F1 + r02 × F2 + r03 × F3 + r04 × F4 = 0
i, j, ˆ
a. Expand in ˆ ˆ k .
b. Group.
c. Get 3 equations (x,y,z).
Try a new point? Try A.
rA1 = rA0 + r01
...
MA = 0
rA1 × F1 + rA2 × F2 + rA3 × F3 + rA4 × F4 = 0
(rA0 + r01 ) × F1 + (rA0 + r02 ) × F2 + (rA0 + r03 ) × F3 + (rA0 + r04 ) × F4 = 0
rA0 × (F1 + F2 + F3 + F4 ) + (r0 1 × F1 + r0 2 × F2 + r0 3 × F3 + r0 4 × F4 ) = 0
rA0 × (F1 + F2 + F3 + F4 ) = 0
F =0
(r0 1 × F1 + r0 2 × F2 + r0 3 × F3 + r0 4 × F4 ) = 0
M0 = 0
So taking moment about a new point gives no additional info.
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