what are the factors affecting a lever?
Answers
Answer:
on one end of a class 1 lever in equilibrium force
F
is applied on a distance
a
from a fulcrum and another force
f
is applied on the other end of a lever on distance
b
from a fulcrum, then
F
f
=
b
a
Explanation:
Consider a lever of the 1st class that consists of a rigid rod that can rotate around a fulcrum. When one end of a rod goes up, another goes down.
This lever can be used to lift up a heavy object with significantly weaker than its weight force. It all depends on the lengths of points of application of forces from the fulcrum of the lever.
Assume that a heavy load is positioned at a length
a
from the fulcrum, the force it pushes down on a rod is
F
.
On the opposite side of a rod at a distance
b
from the fulcrum we apply a force
f
down such that two a lever is in equilibrium.
The fact that a lever is in equilibrium means that the work performed by forces
F
and
f
when a lever is pushed on either side by a small distance
d
must be the same - whatever work we, using force
f
, perform to push down our end of a lever on a distance
b
from the fulcrum should be equal to work to lift a heavy object on a distance
a
on the other end of a lever.
Rigidity of a rod that serves as a lever means that the angle a lever turns around a fulcrum is the same on both ends of a lever.
Assume that a lever turned by a small angle
ϕ
around a fulcrum slightly lifting a heavy weight. Then this heavy weight that exhorts a force
F
on one end of a rod at a distance
a
from a fulcrum was lifted by
a
⋅
sin
(
ϕ
)
height. The work performed must be
W
=
F
⋅
a
⋅
sin
(
ϕ
)
On the other end of a rod, on distance
b
from the fulcrum, force
f
pushed the lever down by
b
⋅
sin
(
ϕ
)
. The work performed equals to
W
=
f
⋅
b
⋅
sin
(
ϕ
)
Both works must be the same, so
F
⋅
a
⋅
sin
(
ϕ
)
=
f
⋅
b
⋅
sin
(
ϕ
)
or
F
f
=
b
a
From the last formula we derive that the advantage of using a lever depends on a ratio between lever ends' distance from fulcrum. The more the ratio is - the more advantage we have and more weight we can lift.