Download Note 11 Working with Forces

Note 11 Working with Forces
The definition of force is best expressed not as what it is but as how it affects motion. The way it
affects motion is described in Newton’s second law of motion. Remember, this is applied to one
object. The net force on that object is equal to the mass of that object times the acceleration of
that object, and both the net force and the acceleration point in the same direction.
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ΣF = ma
A single force will always produce an acceleration. If an object has an acceleration, then the net
force must be non-zero.
If the net force were zero, then the acceleration is zero. This means the velocity is constant. The
object can be at rest or has a constant non-zero velocity. This is the essence of Newton’s first law
of motion.
The unit of force is given the name the newton, N. According to Newton’s second law, the newton
is made up of the following SI units.
⎡ kg ⋅ m ⎤
[N ] = [kg][m/s 2 ] = ⎢ 2 ⎥
⎢⎣ s ⎥⎦
1 N = 0.225 lbf (pound force)
So how is it that the scale shows mass and force together?
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Categories of Force
There are two categories of forces: non-contact and contact forces.
Non-contact forces are those that do not required physical contact. We will deal with only gravity.
Contact forces do required physical contact. For us, these are all other forces that are not gravity.
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Force Vectors
The way to deal with force vectors is to place all of the forces on a single object onto its own
coordinate system centered on the object. This is called a free-body diagram. The label of each
force vector contains a type, a source, and a target. Here are two free-body diagrams of a ball
hung by a string before and after release to free fall.
Ftension from string on ball
ball
Fgravity from Earth on ball
ball
Fgravity from Earth on ball
Some forces have shortcuts. The force from gravity is also referred to as the weight, W, and the
tension force is T.
Tstring on ball
ball
WEarth on ball
ball
WEarth on ball
Lastly, unless there are many forces, the source name can be omitted and the target name is
clear as long as you label the object of the free-body diagram.
T
ball
W
ball
W
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