VCE Physics.comStructures -
• Torque• Centre of mass• Equilibrium• Stability• Tension structures• Arches• Cantilevers• Ties
Structures
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VCE Physics.comStructures -
Torque
• Torque is the “turning effect”• “Moments” are the product of force and radius. These can cause
rotation.• Torque is a vector cross product - it will be perpendicular to F and r.
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! =Fr sin"
10 N
2.0 m
! =2.0m"10N"sin60°=17Nm
60°
10 N x sin 60° = 8.7N
! =20Nm
VCE Physics.comStructures -
Rotational equilibrium
• For the see-saw to be in balance the overall moments must add to zero.
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10 kg
100 N
1.0 m
100 Nm (clockwise)
0.5 m
20 kg
200 N
100 Nm (anti-clockwise)
The centre of mass is over the fulcrum
VCE Physics.comStructures -
Centre of mass
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• The centre of mass is the point at which an object will balance.• This is rotational equilibrium - the sum of the torque around that point is
zero.• A force applied through the centre of mass will not cause a rotation.
30 kg50 kg
2.0 m
4.0 m
x =
m1x1+m2x2 + .....m1+m2 + .....
x =
(50kg!2.0m)+(30kg!4.0m)50kg+30kg x =2.75m
x =
220kgm80kg
x
VCE Physics.comStructures -
Equilibrium
• For a structure to remain stationary:• The forces must be in equilibrium !F = 0 • The torques must be in equilibrium !" = 0
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100 kg
1000 N
6.0 m4.0 m
200 N
Beam mass = 20kgR1 R2
3.0 m
VCE Physics.comStructures -
Equilibrium calculations
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0=(1000N!4m)+(200N!3m)"(R2!6m)
R2!6m =4000Nm+600Nm
R2 =
4600Nm6m
R2 =770N
Find R2: Torque = 0
0=(R1+770N )!(1000N+200N )
R1=1200N !770N
R1=430N
Find R1: Forces = 0
VCE Physics.comStructures -
Stability
• As long as the centre of mass is above part of the base, the structure will not topple.
• This is because the torque acts to return the structure to its original position.
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Rotational equilibrium
Torque will maintain stability, rotating back towards centre
of mass.
Torque will cause the box to continue to topple,
away from centre of mass.
VCE Physics.comStructures -
Arches
• A beam will bend if a load is applied between the supports.• This puts the top in compression & bottom under tension.• It is liable to crack under tension.
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Tension
Compression
VCE Physics.comStructures -
• An arch transmits loads horizontally to the ends. Stone blocks are under compression.
• The arch must be supported horizontally eg by walls or buttresses.
Arches
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Load
Reactions Reactions
VCE Physics.comStructures -
Tension structures
• The vertical & horizontal forces must all be in balance.
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100 N
TT
mg
35°35°
2T sin! =mg
2T sin35°=100N
T =
100N2sin35°
T =87N
50N50N
71N71N
As the vertical angle ! 0°, the tension increases.
87N87N
VCE Physics.comStructures -
Cantilevers
• The sum of the torque around the entry point must be zero.
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100 kg
1000 N200 N
Beam mass = 20kg
2.5 m
1.0 m
0.5 m
4.0 m
F
R
0=(200N!1.0m)+(1000N!2.5m)"(F !0.5m)
F =
200Nm +2500Nm0.5m
F =5400N
0=R !5400N !200N !1000N
R =6600N
Take torques around here!
VCE Physics.comStructures -
1000 N
Ties
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100 kg
1000 N
200 N
Beam mass = 20kg
2.0 m
4.0 m
0=(200N!2m)+(1000N!4.0m)"(T sin30°!4.0m)
T = 400Nm+4000Nm
0.5!4.0m
T =2200N
Take torques around here!
30°
T1100N
1900N
Force in beam is
Fh =1900N Fv =100N
Components of tension:
Tv =T sin30°=1100N
Th =T cos30°=1900N