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Mean = 10.8 (68%)
Sigma = 3 (20%)
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Class 10 - Force and Motion I
Chapter 5 - Wednesday September 16th
•Force and acceleration
•Newton's first law
•Force and mass
•Newton's second law
•Some particular forces
Reading: pages 87 thru 99 (chapter 5) in HRW
Read and understand the sample problems
Assigned problems from chapter 5:
24, 26, 34, 38, 44, 46, 52, 56 (due Sun. Sept. 26)
What causes acceleration?
Linguistic arguments:
• Some sort of interaction - loosely speaking, a push or a
pull on an object.
• We call this a force, which can be said to act on a body.
• Examples of forces:
Normal or "contact force"
Gravitational force
Electromagnetic force
Weak and strong nuclear forces
We'd better be more
scientific about this...
Before Newton
•Friction and air resistance have a tendency to distort
our appreciation of the nature of forces.
•Think of a motor boat or a car: their engines constantly
do work (i.e. generate driving forces) in order to maintain
a constant velocity.
•This led people to believe, before Newton, that a force
was necessary to keep a body moving at constant velocity,
and that the natural state of a body was when it was
stationary - this leads to some very interesting
philosophical questions.
But hang on a minute.... What happens if
we remove all resistance to motion, i.e.
friction and air resistance?
Newton's first law
If no force acts on a body, then the body's velocity
cannot change; that is, it cannot accelerate.
An object at rest tends to stay at rest and an
object in motion tends to stay in motion with the
same speed and in the same direction unless acted
upon by an unbalanced force.
•Therefore, according to Newton, the car traveling at
constant velocity experiences no net or unbalanced force.
•That is, the engine forces it one way, and friction
exactly balances this force by opposing the motion with
an equal and opposite force.
•Friction is a somewhat mysterious force, though we will
learn to deal with it in the next chapter.
Force
Definition (there is no proof!):
•We declare that: a force of 1 Newton is that force
required to accelerate our standardized mass (1 Kg) at a
rate of 1 m.s-2.
•A reference defines the Kg, and the above definition
defines force.
•Force is a vector. Thus, forces add like vectors. This is
something one has to test by experiment.
•Forces obey the "principle of superposition.“
Ftotal   Fi
i
Free-body diagrams
F1
F1
S
F3
F2
F2
F3
F  0
•The forces shown above are what we call "external forces."
•They act on the "system" S.
•S may represent a single object, or a system of rigidly
connected objects. We do not include the internal forces
which make the system rigid in our free body diagram.
Inertial reference frames
An inertial reference frame is one in which Newton's
laws hold.
Simply put: this is a frame which is not accelerating.
aPA
dvPB dvBA


 aPB
dt
dt
 FPA  FPB
*
*Assuming we define mass in the same way in all inertial frames
•Newton's laws do not apply in accelerating frames.
•They must also be modified in relativistic and quantum limits
What is mass?
This is not a trivial question!
•On earth, we use the fact that the acceleration due to
gravity is approximately constant for all objects, and
characterize an “effective” mass according to the force
needed to balance the earth's gravitational force.
•We call this "weight", as measured in Newtons (v. imp!)
•In outer space, everything is weightless, but not massless!!
Mass is simply the characteristic of a body that relates
a force on the body to the resulting acceleration
•This is how one has to measure mass in outer space.
•No static method works, because there is no basis for
comparison, e.g. hanging or spring balances, which depend on g.
•YOUR MASS DOES NOT CHANGE IN OUTER SPACE!!!
Newton's second law
This law was developed through systematic experimentation
1) We calibrate our force apparatus by accelerating our
standard mass by 1, 2, 3, etc.. m.s-2.
2) We then apply a standard force of 1 N to a range of
objects, and measure their acceleration.
3) We then look for the relationship between force, mass and
acceleration.
And the result:
Fnet, x  max ,
Fnet   Fi  ma
5  1
i
Fnet, y  ma y ,
•We may treat the components separately.
•Mass is a scalar quantity.
•1 N = (1 Kg)(1 m.s-2) = 1 Kg.m.s-2
Fnet, z  maz
Gravity:
Some particular forces
•During free fall
a   g ĵ

F  ma  mg ĵ
•This is always true at the surface of the earth, and will
usually be the case for problems worked in this class.
•In other words, even when a mass is stationary on the
surface of a table, gravity still acts downwards with a
magnitude equal to mg.
•This leads to the concept of a normal force: for the mass
on the table to remain stationary, the table must exert an
upward force on the mass so as to exactly balance the force
due to gravity.
Normal force
N  Fg  ma
N  Fg  ma y
N  ma y  Fg  m  a y  g 
Weight (a force!):
N  Fg  mg if a y  0
•In the above example, the internal forces within the table
supply the normal force.
•If we hold the mass in a stationary state, we must supply
the force. This is the sensation of weight, i.e.
W  Fg  mg Newtons