Forces and equilibrium - Orthopaedic Biomaterials in Research and Practice - page 13

the line of action of A . Further, suppose that the cube has a mass of 100 g
(0.1 kg).
A change in either speed or direction of motion is called acceleration.
The change in acceleration over a period, if constant, can be determined
by measuring the velocity of an object at two separate points in time
(Figure 1.9). Initially, we locate the cube and measure its speed as 1 m/s
in the left direction. Then, 1 s later, we measure its speed as 3 m/s in
the same direction. The speed (magnitude of velocity) has increased by
2 m/s. This change in velocity is only possible because of an external
force.
Newton's second law states, in a very familiar form:

F = m ∙ a

That is, a , the acceleration of an object with mass m , is directly related
to the force that is applied to that object. Since force is a vector and mass
is a scalar, acceleration must also be a vector, pointing along the line of
action of the force.
Thus,

Fma =⋅ .

In this case, an object with a mass of 0.1 kg experiences acceleration
(change in magnitude of velocity) of 2 m/s in 1 s. This can be accounted
for by a force of 0.2 N acting in the direction of the velocity for the inter-
vening second. In fact, by knowing the mass and observing the change
in velocity, we infer the presence of the force. This is the only way we
have of directly perceiving the presence of a net resultant force. Thus,
it should come as no surprise that a newton is defined as the force that
produces an acceleration of 1 m/s per second (1 m/s 2 ) when applied to
an object with a mass of 1 kg and that the intrinsic units of the newton
are kg ∙ m/s 2 .

v

0.1 kg

Location
after 1 s

Initial
location

| v | = 3 m/s | v | = 1 m/s

us | a | = 2 m/s 2

and | F | = m | a | = 0.2 N

FIGUre 1.9 newton's second law.