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5-1 NEWTON’S FIRST AND SECOND LAWS 99

force components along the xaxis and is completelyunrelated to force compo-
nents along another axis. In general,

The acceleration component along a given axis is caused only bythe sum of the force

components along that sameaxis, and not by force components along any other axis.

Table 5-1Units in Newton’s Second Law (Eqs. 5-1 and 5-2)

System Force Mass Acceleration

SI newton (N) kilogram (kg) m/s^2

CGSa dyne gram (g) cm/s^2

Britishb pound (lb) slug ft/s^2

a1 dyne1gcm/s (^2).
b1lb1 slugft/s (^2).
Checkpoint 2
The figure here shows two horizontal forces acting
on a block on a frictionless floor. If a third horizon-
tal force also acts on the block, what are the magnitude and direction of when
the block is (a) stationary and (b) moving to the left with a constant speed of 5 m/s?
F
:
F 3
:
3
3 N 5 N
Forces in Equilibrium.Equation 5-1 tells us that if the net force on a body is
zero, the body’s acceleration. If the body is at rest, it stays at rest; if it is
moving, it continues to move at constant velocity. In such cases, any forces on the
bodybalanceone another, and both the forces and the body are said to be in
equilibrium.Commonly, the forces are also said to cancelone another, but the
term “cancel” is tricky. It does notmean that the forces cease to exist (canceling
forces is not like canceling dinner reservations). The forces still act on the body
but cannot change the velocity.
Units.For SI units, Eq. 5-1 tells us that
1N(1 kg)(1 m/s^2 )1kgm/s^2. (5-3)
Some force units in other systems of units are given in Table 5-1 and Appendix D.
Diagrams.To solve problems with Newton’s second law, we often draw a
free-body diagramin which the only body shown is the one for which we are sum-
ming forces. A sketch of the body itself is preferred by some teachers but, to save
space in these chapters, we shall usually represent the body with a dot. Also, each
force on the body is drawn as a vector arrow with its tail anchored on the body. A
coordinate system is usually included, and the acceleration of the body is some-
times shown with a vector arrow (labeled as an acceleration). This whole proce-
dure is designed to focus our attention on the body of interest.
:a 0
External Forces Only.Asystemconsists of one or more bodies, and any
force on the bodies inside the system from bodies outside the system is called an
external force.If the bodies making up a system are rigidly connected to one an-
other, we can treat the system as one composite body, and the net force on it
is the vector sum of all external forces. (We do not include internal forces— that
is, forces between two bodies inside the system. Internal forces cannot accelerate
the system.) For example, a connected railroad engine and car form a system. If,
say, a tow line pulls on the front of the engine, the force due to the tow line acts on
the whole engine – car system. Just as for a single body, we can relate the net ex-
ternal force on a system to its acceleration with Newton’s second law, ,
wheremis the total mass of the system.

F

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