LESSON 1.13 - STABILITY
Overview
This lesson deals with factors that affect the stability
of objects. On completion of the lesson, you should be
able to describe the center of gravity of an object and
explain how the center of gravity of an irregular object
can be determined. You should also be able to explain why
objects topple under certain conditions.
ACTIVITIES
- Use a plastic funnel
to illustrate stable, unstable and neutral
equilbrium.
- Locate the center of
gravity of an irregularly shaped piece of
cardboard or
plywood.
Center
of mass
If the masses of all the particles that make up a body
are multiplied by their distances from the center of
mass, the net result would be zero. (A convention needs
to be used in which distances in one direction are
assigned a positive value and distances in the opposite
direction are assigned a negative value.)
All of the body’s
mass can often be considered as being concentrated at
this point.
Center
of gravity
If the weights of all the particles that make up a body
are multiplied by their distances from the center of
gravity, the net result would be zero. (A convention
needs to be used in which distances in one direction are
assigned a positive value and distances in the opposite
direction are assigned a negative value.)
All of the body’s
weight can often be considered to be concentrated at this
point. Because weight depends on gravity and the force of
gravity varies with distance from the center of the
earth, the center of gravity of a very tall building can
differ slightly from its center of mass.
Stable
equilibrium
An object is in a state of stable equilibrium if a small
displacement or rotation raises its center of gravity.The
weight of the object and the reaction from the point at
which it is supported form a couple that cause the object
to rotate back to its original position.
An object is in unstable
equilibrium is a small displacement or rotation lowers
its center of gravity. In this case, the couple formed by
the weight of the object and the reaction at its point of
support cause it to rotate further from its original
position.
Toppling
If an object is rotated so that a vertical line drawn
through its center of gravity does not pass through its
base, the object will topple. Toppling is caused by a
couple consisting of the object’s weight and the
reaction from its point of support.
Buoyancy
When an object is partially or completely immersed in a
fluid, it experiences an upward force equal to the weight
of the fluid displaced by the object. If the weight of
the object is less than the weight of the fluid it
displaces, it will move upwards or float on the surface
of the fluid.
The center of buoyancy is
the center of gravity of the body of fluid that it
displaces.
If the center of gravity
of a floating object is above the center of buoyancy, it
will topple. For a floating object to be stable, its
center of gravity must always be at a lower level than
its center of buoyancy.
Review
Questions
- Give examples of
objects that are in:
a) Unstable
equilibrium,
b) Stable equilibrium
and
c) Neutral equilibrium
- Does the center of
gravity of an object always need to be on or
inside the object?
- What is the
difference between the center of gravity and the
center of mass? Under what conditions do these
differ?
- Why do double-decker
busses not tip over easily?
- Which glass shown
below is likely to topple first if the angle of
incline is increased? Why?
- The centers of
gravity of three busses parked along an incline
are shown on the diagram below. Which bus will
topple first if the angle of incline is
increased? Which will be the next to topple?
- Under what conditions
will a floating object become unstable and tend
to capsize?
ACTIVITIES
- Use a plastic funnel
to illustrate stable, unstable and neutral
equilbrium.
- Locate the center of
gravity of an irregularly shaped piece of
cardboard or
plywood.
ACTIVITY
#1 Stable, Unstable & Neutral Equilibrium
Purpose: To
illustrate stable, unstable and neutral equilibrium using
a plastic funnel
Equipment:
Plastic funnel (If there
is a tab on the edge of the funnel, cut it off.)
Ballpoint pen that fits
snugly in the small end of the funnel
Procedure:
- Place the funnel with
the spout pointing upwards on a table. Show that
one edge can be lifted slightly without toppling
the funnel.
- Place the pen in the
narrow section of the funnel – with the
point jutting out.
- Show that it can not
be balanced on the point of the pen. This is an
example of unstable equilibrium. (Even without
the pen, balancing the funnel on the narrow end
results in unstable equilibrium.)
- Allow the funnel to
roll around on its side. This illustrates neutral
equilibrium.
ACTIVITY
#2 Locating the center of gravity
Purpose: To find
the center of gravity of a flat object.
Equipment:
Cardboard or plywood
object with an irregular shape.
Drill.
String
Small weight
Small nail
Procedure:
- Drill 3 holes more or
less equally spaced around the perimeter of the
object
- Place the nail
through one of the holes, tie the string to the
nail and attach the weight to the string.
- The object should be
able to move freely while suspended from the nail.
- Draw a vertical line
on the object in line with the string.
- Repeat the procedure
while suspending the object from another hole.
- Do this a third time.
- The three lines
should cross at the same point. This is the
center of gravity of the object.
.
.
HANDS-ON
HOMEWORK
Select one or more of the recommended
activities for Lesson 1.14, collect the items needed and test the
procedure before demonstrating the activity during the
next theory lesson.
Lesson 1.14
Stability
- a) A cone balanced on
its point.
b) A cone standing on its circular end.
c) A cone that can roll on its side.
- No, the centers of
gravity of horse-shoe’s and boomerangs are
in the space outside of the object.
- The center of mass is
a point at the center of an object’s
distribution of mass. The mass of the body can
often be regarded as being concentrated at that
point. The center of gravity is a point at the
center of an object’s distribution of weight.
Unless the object is very large, the center of
mass is located at the same point as the center
of gravity
- They have low centers
of gravity.
- The glass with the
liquid in it. It's center of gravity is higher
than that of the empty glass. As the angle is
increased, the center of gravity of the glass
with liquid will move past the edge supporting
the glass.
- Not clear. The middle
bus will be the last to tip.
- If the center of mass
moves to above the center of buoyancy.
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