Forces and equilibrium - Orthopaedic Biomaterials in Research and Practice - page 15

in turn, to the bone. The change in momentum is related to the force it
applies to the bone:

F ∙ t = Δ m ∙ v

The quantity F ∙ t , the average force times the time it acts, is called the
impulse , whereas Δ m ∙ v is the magnitude of the change of momentum
during time t . Thus, if the momentum is transferred in 1 s, it will produce
a force of 0.05 N acting during that period; if it is transferred in 0.001 s
(1 ms) it will produce a force of 50 N during that period. The impulse is
constant for any change in momentum; the resulting force is determined
by the time over which the change in momentum takes place.

PROBLEM 1.5
Suppose that the mallet in Figure 1.10, instead of coming to rest,
rebounds in the opposite direction with a speed of 0.05 m/s. Assuming
that the period of force application to the bone is unchanged, does the
force on the bone

A. Remain unchanged?

B. Decrease by 50%?

C. Increase by 50%?

D. Double?

E. None of the above

ANSWER:
The answer is C. The change in momentum is now 0.05 + 0.025 or 0.075
N ∙ s. Since the change in momentum and thus the impulse increases by
50%, if all other conditions remain the same (as stated), then the force
must increase by 50%.

Coefficient
of restitution

The ratio of the final relative speed of the mallet and osteotome to their
initial speed is called the coefficient of restitution ( e ). It is a character-
istic of any pair of materials and may take on values between one and
zero. In the text case of the mallet striking the osteotome, e = 0, whereas
in Problem 1.5, e = 0.5 (with an obvious change in material of one object
in the example). Clearly, as e increases, the impulse and possible resul-
tant forces increase. We can easily feel the difference between walking
on a hard surface (large e , small t ) and a soft surface (small e , large t ).
A direct conclusion is that objects in contact transmit smaller forces
than ones that can rebound and separate, producing larger impulses.
The increased force in a rebound situation (compared with that in a full-
contact situation) is often called an inertial force , reflecting its origin in
a change in momentum.

Conservation
of energy

The last principle that we must consider related to dynamics is that of
conservation of energy. A moving object with a mass m and a velocity