More on Newton’s
rd
3
Law
Conceptual Example:
What exerts the force to move a car?
Response: A common answer is that the engine
makes the car move forward. But it is not so simple.
The engine makes the wheels go around. But if the
tires are on slick ice or deep mud, they just spin.
Friction is needed. On firm ground, the tires
push backward against the ground because of
friction. By Newton’s 3rd Law, the ground
pushes on the tires in the opposite direction,
accelerating the car forward.
Helpful Notation
On forces, the 1st subscript is the object that the
force is being exerted on; the 2nd is the source.
Action-Reaction Pairs
act on
Different Objects!
Conceptual Example
Action-Reaction Pairs
Act On Different Objects
• Forces exerted BY an object DO NOT
(directly) influence its motion!!
• Forces exerted ON an object (BY some
other object) DO influence its motion!!
• When discussing forces, use the words
“BY” and “ON” carefully.
Weight & Normal Force
Weight  The force of gravity on an object.
Write as FG  W.
• Consider an object in free fall.
Newton’s 2nd Law is:
∑F = ma
• If no other forces are acting, only FG ( W) acts
(in the vertical direction).
Or:
∑Fy = may
(down, of course)
• SI Units: Newtons (just like any force!).
g = 9.8 m/s2  If m = 1 kg, W = 9.8 N
“Normal” Force
• Suppose an object is at rest on a table.
No motion, but does the force of
gravity stop? OF COURSE NOT!
• But, the object does not move:
2nd Law  ∑F = ma = 0
 There must be some other force
acting besides gravity (weight) to
have ∑F = 0.
• That force  Normal Force FN (= N in your text!)
“Normal” is a math term for perpendicular ()
FN is  to the surface & opposite to the weight
(in this simple case only!) Caution!!!
FN isn’t always = & opposite to the weight, as we’ll see!
Normal Force
• Where does the normal force
come from?
Normal Force
• Where does the normal force
come from?
• From the other object!!!
Normal Force
• Where does the normal force
come from?
• From the other object!!!
• Is the normal force ALWAYS
equal & opposite to the weight?
Normal Force
• Where does the normal force
come from?
• From the other object!!!
• Is the normal force ALWAYS
equal & opposite to the weight?
NO!!!
An object at rest must
have no net force on it.
If it is sitting on a table, the
force of gravity is still there;
what other force is there?
Free Body
Diagram
Show all forces
in proper
directions.
The force exerted
perpendicular to a
surface is called the
Normal Force FN.
FN is exactly as large as needed to balance the force from the
object. (If the required force gets too big, something breaks!)
∑F = ma = 0 or Newton’s 2nd Law for Lincoln:
FN – FG = 0 or FN = FG = mg
Note! FN & FG AREN’T action-reaction pairs from N’s 3rd
Law! They’re equal & opposite because of N’s 2nd Law!
FN & FN ARE the action-reaction pairs!!
Example
The normal
force is NOT
always equal
& opposite
to the weight!!
m = 10 kg
Find: The normal force on the
box from the table in Figs. a, b, c.
Always use N’s 2nd Law
to CALCULATE FN!
Example
What happens when a person pulls
up on the box in the previous
example with a force of 100.0 N?
The box will accelerate
upward because
FP > mg!!
Note: The normal force is zero
in this case because the mass
isn’t in contact with a surface.
m = 10 kg
∑F = ma. FP – mg = ma
100 – 98 = 10a
a = 0.2 m/s2
Example : Apparent “weight loss”
A 65-kg woman descends in an elevator that
accelerates at 0.20g (= 1.96 m/s2) downward.
She stands on a scale that reads in kg.
(a) During this acceleration, what is her weight
& what does the scale read?
(b) What does the scale read when the elevator
descends at a constant speed of 2.0 m/s?
• Note: To use Newton’s 2nd Law for her, ONLY the forces
acting on her are included. By Newton’s 3rd Law, the
normal force FN acting upward on her is equal & opposite
to the scale reading. So, the numerical value of FN is equal
to the “weight” she reads on the scale! Obviously, FN here
is NOT equal & opposite to her true weight mg!!
How do we find FN? As always
We apply Newton’s 2nd Law to her!!
Example : Apparent “weight loss”
Mass m = 65-kg, mg = 637 N
Acceleration a = 1.96 m/s2 down.
(a) During acceleration, what is her weight
& what does the scale read?
(b) Answer part a if the elevator descends at
a constant speed of 2.0 m/s?
• Due to Newton’s 3rd Law, the numerical value of FN is
equal to the “weight” she reads on the scale! Obviously,
FN is NOT equal & opposite to her true weight mg!!
Find FN by applying Newton’s 2nd Law to her!!
• Let down be positive so up is negative: Fy = ma
 mg – FN = ma  FN = m(g – a) = (65)(9.8 – 1.96) = 509.6 N
(FN/g)= 52 kg = Scale Reading in kg
= “Effective Weight”!