Example: Ladder Leaning Against a Wall
Statics, FBD, Stability
Given: A ladder leans against a frictionless
wall.
Required: Angle between ladder and ground
when it starts to slip.
How much does the
Leaning Tower of Pisa lean?
1.
2.
3.
4.
5.
1°
2°
3°
4°
5°
Moment of NW about
base is:
1. NWL
2. NWLsinθ
3. NWLcosθ
4. NWLtanθ
5. NWLsinθ + NWLcosθ
EF 152 Spring, 2010 Lecture 1-3
Example: Step Ladder
Moment of NW about
base is:
1. Positive
2. Negative
1
56 kg
EF 152 Spring, 2010 Lecture 1-3
Example: Step Ladder
2
56 kg
Given: A 56 kg person stands on a 14 kg stepladder.
The person is 2.0 m high on the ladder, measured
along the rail. The tie rod is halfway up the ladder.
Assume no friction with the floor, and that the mass
of the ladder is uniform. Simplify as a 2D problem.
Required: (a) Force in tie rod (b) normal force of
ground on each side of the ladder
EF 152 Spring, 2010 Lecture 1-3
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EF 152 Spring, 2010 Lecture 1-3
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Stability
Stability
If an object is on an incline and the
only force on it is its weight,
it will tip if:
_____________________________
If an object is in equilibrium, and given a small displacement,
there are three possibilities:
•
•
•
_______ equilibrium: object returns to original position
Example: ball hanging from a string
__________ equilibrium: object moves further away
from original position
Example: pencil balanced on point
_________ equilibrium: object stays at new position
Example: sphere on a flat table
Stable
Unstable
To determine tipping with arbitrary loads, sum moments
about the each extreme and assume the normal force to be
located at that point. If the resultant moment would cause
the object to fall away from the support area, then the object
will tip.
Neutral
EF 152 Spring, 2010 Lecture 1-3
Example: Stability
For tipping calculations you need to be careful with the
‘normal force’ location. Its location should be assumed to be
point at which the object might tip.
5
Center of mass
A truck is parked on an inclined
1.6 m
road as shown. Determine the
slope of the road that causes the
truck to tip over.
2.4 m
θ
2.2 m
EF 152 Spring, 2010 Lecture 1-3
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EF 152 Spring, 2010 Lecture 1-3
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