PHYSICS

3.3.4. The Lever
A lever is the simplest mechanism by which it is possible to
balance a larger force by a lesser one. A lever consists of a plank
which pivots at a point called the fulcrum. There are three forces
acting on the plank: the downward force (F) used to try to lift
the heavy mass (M), the reaction force (R) at the fulcrum, and
the force (P) arising from the gravitational pull on the body
(fig. 3.3).
R
M
Muscle
(J
Humeral
bone
p
5x
F
'------­
/]
Fig. 3.3. A lever which consists of a plank of mass M pivoted
near its end can be used to mechanical advantage; /] and /] are the
lever arms; R is the reaction force at the fulcrum
Two of these forces, F and P, tend to rotate the plank about
the fulcrum, the extent of which depends on the product of the
force and its perpendicular distance from the fulcrum. The
product is called the moment of the force and the plank will be in
equilibrium when the clockwise and counterclockwise moments
are equal:
Fl, = PI]
P
(3.31)
Hence, F will be small if I] is small, in which case the point
of pivot should be as near the body as possible. The ratio PI/F is
known as the mechanical advantage of the lever.
The biceps muscles and the jaws are examples of a lever mechanism
in a living organism.
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a
Fig. 3.4. Lever which is composed with radial and humeral bones
and muscle: a - diagram of biceps muscles lifting a weight in his
hand; b - the mechanical model for this system: F is the upward
force of the biceps; R is the downforce of the joint; P is the
weight; I] and /] are the lever arms
Example. Consider the diagram of the biceps muscles which lift a
weight 6 N held in the hand (fig. 3.4). The biceps, the flexor muscle of
the forearm, is at an angle of (J = 12° to the elbow. Find the force
exerted by the biceps.
Solution. The component of the force exerted by the biceps muscles
that is perpendicular to the lever is Feese. The equation of equilibrium
of lever moments is:
p. II = F· I]
6 N . 5x = Fxcosl2°
F = 30
0.978 = 30.7 N
b
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