engineering mechanics - equilibrium
DESCRIPTION
Engineering Mechanics - EquilibriumTRANSCRIPT
2-Particle Interactions
1
2
f21
f12
Sun : earth
Atom : atom
12 21= −f f
12 21+ =f f 0
3-Particle Interactions
1
2f21
f13
ij ji+ =f f 03
f12
f31
f23
f32
F3
F1
F2, 1, 2,3i j =
Many-Particle Interactions
1
2f21
f13
3
f12
f31
f23
f32
F3
F1
F2
i ijj i≠
+ =∑F f 0 1,2,i =
i iji i j i≠
+ =∑ ∑∑F f 0
Summation of the above equation gives
Newton’s 3rd law
iji j i≠
=∑∑ f 0
Therefore:
ii
=∑F 0
For an N particles system, in equilibrium
Newton’s 1st law
Free-Body-Diagram
Isolate the body in question with the representation of all external forces acting on it.
ii
=∑F 0
Problem 1
Remove Spike from Timber
It is desired to remove the spike from the timber by applying force along its horizontal axis. An obstruction A prevents direct access, so that two forces, one is 1.6kN and the other P, are applied by cables as shown. Compute the magnitude of P necessary to ensure axial tension T along the spike. Also find T.
Remove Spike from Timber
T
sin 1.6sinP a β=
αβ
Horizontal:
Vertical:
cos 1.6cosT P a β= +
Problem 2
Knot in Static Equilibrium?
Mass: m
α β
F1 F2
1 2cos cosF Fα β=
1 2sin sinF F mgα β+ =
Horizontal:
Vertical:
When strings are almost straight horizontally
1
2
cossin cos cos sin
cossin cos cos sin
F mg
F mg
βα β α β
αα β α β
=+
=+
when00
αβ→→
1
2
FF→∞→∞
Mass: m
α β
F1 F2