Physics 170 - Mechanics
Lecture 26
Static Equilibrium
Zero Torque & Static Equilibrium
Static equilibrium occurs when an object is at
rest, neither rotating nor translating.
Center of Mass & Balance
If an extended object is to be balanced, it
must be supported through its center of mass.
Balance
An object balances when the pivot point is located directly under
(or over) the center of mass. For that situation, τgrav=0.
Zero Torque & Static Equilibrium
If the net torque is zero, it doesn’t matter
which axis we consider rotation to be around; we
are free to choose the one that makes our
calculations easiest.
Zero Torque & Static Equilibrium
When forces have both vertical and horizontal
components, in order to be in equilibrium an
object must have no net torque, plus no net force
in either the x- or y-direction.
Example: Remote Control
A 0.102-kg remote control h=24.4 cm
long rests on a table, as shown, with a length
L overhanging its edge. To operate the power
button on this remote requires a force of
0.260 N.
How far can the remote control
extend beyond the edge of the table and
still not tip over when you press the power button?
Assume the mass of the remote is distributed
uniformly, and that the power button is on the end
of the remote overhanging the table.
Example: Diving Board
A diving board (L=4.64 m) is
supported by two pillars. One pillar is
at the left end of the diving board,
as shown; the other is d = 1.54 m away.
Find F1 and F2 if the swimmer stands
at the left end of the diving board.
Assume that the diving board is uniform
and has a mass of 81 kg and the diver
has a mass of 88.7 kg.
Example: Walking the Plank
A cat walks along a uniform plank that
is 4.00 m long and has a mass of 7.00 kg.
The plank is supported by two sawhorses,
one a 0.440 m from the left end of the
plank and the other 1.50 m from the
right end. When the cat reaches the
right end, the plank just begins to tip.
What is the mass of the cat?
Example: Rod Seat
A m=45.5 kg uniform rod L=4.24 m long is attached to
a wall with a hinge at one end. The rod is held in a
horizontal position by a wire attached to its other end.
The wire makes an angle of θ=31.2° with the horizontal,
and is bolted to the wall directly above the hinge.
If the wire can withstand a maximum tension of
T=1420 N before breaking, how far x from the wall can a
M=68.0 kg person sit without breaking the wire?
T
31.2°
mg
Mg
Example: Rod and Wire
A rigid vertical rod of length L
and negligible mass is connected to
the floor by a bolt through its
lower end. The rod also has a 45°
wire connecting its top end to the
floor.
If a horizontal force F is applied to the center of the rod,
find the tension in the wire.
Find the horizontal and vertical components of the force
exerted by the bold on the rod.