Center of Gravity
 The point at which the sum of the weights of all
particles that compose the matter may be
concentrated.
How to Determine the Center of Gravity
1. Uniform objects – geometric center
2. Non uniform objects – by hanging or plumb-line
method
3. CG outside the body – the weight of the object can
still be considered to act at this point even if it is not
on the body of the object. Example, hanger, ring,
doughnut
Equilibrium
 An object is said to be in equilibrium if it is in a state of
balance
States of equilibrium
1. Stable – the object cannot be easily toppled down
2. Unstable – the object can be easily toppled down
3. Neutral – the object can roll from one side to the
other
Factors that Affect Equilibrium
Conditions
Position of center of gravity – the lower the center of
gravity, the more stable
2. Area of the base – the wider the base, the more
stable
3. Mass of the object – the higher the mass, the more
stable
1.
Conditions of Equilibrium
1st Condition – the sum of all forces = 0
2nd condition – the sum of the torques = 0
Torque (τ) = product of the force and lever arm
τ = Fxl
Sample Problems
A car weighing 2000N on a bridge is 6.0m from one
end of the bridge piers and 4.0 m from the other.
How much force does each pier of the bridge exert to
support the car?
2. A 75 kg adult sits at one end of a 9.0 m long board.
His 25-kg child sits on the other end.
a. Where should the pivot be placed so that the
board is balanced (neglecting the board’s mass)
b. Find the pivot point if the boarddis uniform and
has a mass of 15.0 kg.
1.
Sample Problems
3. A girl weighing 450N sits on one end of a seesaw that
is 3.0m long and is pivoted 1.3m from the girl. If the
seesaw is just balanced when a boy sits at the opposite
end, what is his weight in N? (Neglect the weight of
the seesaw)
Assignment
1.
A farmer sells sweet potatoes in the market. He and
his son place sweet potatoes in a sack and carry it on
a uniform piece of bamboo, 3.0 m long. The bamboo
weighs 19.6N and the sack with potatoes weighs
490N. The farmer carries a load of 294N. (The
bamboo is carried at the ends by the farmer and the
son) Determine:
a. the load carried by the son
b. how far from the farmer’s end should be load be
placed?
Assignment
2. Three children are trying to balance a seesaw which
consists of a fulcrum rock, acting as a pivot at the
center and a very light board 3.6 m long. Two
playmates are already on either end. Boy A has a mass
of 50 kg and girl B has a mass of 35 kg. Where should
girl C, whose mass is 25 kg. place herself so as to
balance the seesaw.