Chapter 5 Newton's Laws of MotionSection 5.2 - 4 Newton's Three Laws of Motion

1) An object's motion (or state of rest) remains constant along a straight line unless theobject is acted upon by a net external force.

2) F→

Net = Σ F→

= m a→

(Σ = "sum of") . This law allows you to calculate the accelerationonce the forces are known. With the acceleration known, you can determine anykinematic quantities needed (displacement, velocity).

3) For each applied force there is an equal but opposite reaction force:

F12→   = – F21

→  

Notes on the three laws:

• The first law is a special case

where Fnet→     = 0 implies a

→ = 0 of the second law.

• The second law is a vector expression, so you must keep track of the components.The net force that appears in the second law is the vector sum of those forces actingON the object. The object may be exerting forces, but only those forces acting onthe object determine the object's change in motion (or lack of it).

• The third law: An action-reaction pairof forces will act on two differentobjects.

See the example at right as well as thetext examples 5-3 and 5-4 which eachshow an action-reaction pair. (Thereare two sets of action-reaction pairs inthe figure at right, but only one set isshown.)

F = W

FGF

Action -reaction pair:

Force exerted BYground ON feet of person

Force exerted BY feet of person ON ground

→

FG → →

Note that, just as in the example above, the normal force

N→ = FGF→     is always

perpendicular to the surface through which the normal force is exerted.

Section 5.6

Weight and mass Weight and mass are physically different quantities. To confuse onefor the other is like thinking that distance is the same thing as velocity. Weight is aforce. Mass is a fundamental measure of the quantity of matter in an object. The weightof an object is proportional to the object's mass: W

→ = m g

→ . The constant of

proportionality here is the acceleration due to gravity (g). Thus, weight (a force) hasunits of mass times acceleration and should never be confused with the mass itself. Themass of an object doesn't change from one location (the earth) to another (the moon),but weight does (because the acceleration due to gravity changes).

Apparent Weight Any device that can accelerate vertically (e.g. an elevator) canproduce the effect of apparent weight. A scale will register the apparent weight (Wa) as

the upward force exerted on your feet by the elevator. From Newton's second law, anobject accelerated vertically will have: ma = Wa – W or Wa = W + ma.

From this follows the observations: 1) Wa > W for upward acceleration (a = +) and 2)Wa < W for downward acceleration (a = –).

Section 5.7

Normal Forces Normal forces are typically support forces, i.e. the force required tosupport an object against the force of gravity and any other applied forces. The normalforce direction is always perpendicular to the surface the object lies upon or is pressedagainst. Two examples:

Example 5-13 F

W

Nθ

Σ F = 0 = N + F sin θ – W

Thus, N = W – F sin θ < W(and reducing N reduces the frictional force [see section 6.1])

up

F

N

W

Object on an inclined plane (with no frictional or other applied forces) The figurebelow shows the relationship between the angle of inclination (θ) and the normal andweight vector directions. Note also that the x-y axes have been rotated so that the x axisaligns with the inclined plane. This makes it easier to describe any motion along theplane with a single coordinate x.

W

N

θ

W cos θ

θ

θ

W sin θ

x

y