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Type: Double
Date: ______________
Objective: Equilibrium Applications, Normal Force and
Weight
Equilibrium Applications, Friction and Newton’s
Laws
Homework: Assignment (1-14)
Do CONCEPT QUESTIONS #’s (16, 25, 26) Ch. 4
AP Physics “B”
Mr. Mirro
Date: ________
Equilibrium, Normal Force and Apparent Weight
<i> The Normal Force
∑ Fy ⇒ may
- F1 - F2 + FN = 0
So,
FN = F1 + F2
<ii> Apparent Weight
∑ Fy ⇒ may
∑ Fy = + FN – W = may
∑ Fy = + FN – mg = may
FN = mg + may
Apparent
Weight
True
Weight
FN = m(g + ay)
AP Physics “B”
Mr. Mirro
Date: ________
Equilibrium, Normal Force and Apparent Weight
Ex 1: In a circus balancing act, a woman performs a headstand on top of a man’s head. The woman
weighs 490 N (≈120 lbs), and the man’s head and neck weigh 50 N. It is primarily the seventh
cervical vertebra in the spine that supports all the weight above the shoulders. What is the normal
force that this vertebra exerts on the neck and head of the man (a) before the act and (b) during the
act ? [Cutnell4.8]
Ex 2: A passenger of mass m = 72.2 kg stands on a platform scale in an elevator cab. [Halliday5.12]
a. What does the scale read if the cab is at rest or moving
with constant speed ?
b. What does the scale read if the cab has an upward
acceleration of magnitude 3.2 m/s2 ?
c. What does the scale read if the cab has an downward
acceleration of magnitude 3.2 m/s2 ?
d. What does the scale read if the cable breaks, so that
the cab falls freely ?
e. What would happen if the cab were pulled downward
with an acceleration of -12 m/s2 ?
0N
2000 N
Ex 3: A 60 kg stunt pilot getting ready for a spectacular trick ascends with a constant acceleration of
a = 15 m/s2. [General]
a. What is the normal force between the pilot and his seat ?
b. What is the g-force on the pilot ?
AP Physics “B”
Mr. Mirro
Date: ________
Equilibrium, Friction and Newton’s Laws I
When a stationary object is in contact with a surface, there is a perpendicular force acting
on the object called the “normal force.”
When the object moves, or attempts to move along the surface, there is also a parallel
component of force called the frictional force or simply “friction.”
In many situations, considerable engineering effort is expended trying to reduce friction.
Oil is used to reduce friction, wear and tear in pistons and cylinder walls in an
automobile engine.
Sometimes friction is necessary !
Without friction, car tires could not provide the traction needed to move a car or
brakes could not stop it !
Surfaces that appear to be highly polished can actually look quite rough at the atomic
level.
Microscopic bumps impede motion as the electric forces between surfaces actually form
chemical bonds or “cold-welds”.
Sliding the object across a surface is often jerky due to the making and breaking of these
bonds.
<i> Static and Kinetic Friction
a. Static Frictional Force
The magnitude Fs of the static frictional force can have any value from “zero” up
to a maximum value of “Fs max,” depending on the applied force.
Fs ≤ Fs max FN
Where, Fs max = μsFN
Where (μs) is the coefficient of static friction and (FN) is the magnitude of the normal force.
b. Kinetic Frictional Force
The magnitude Fk of the kinetic frictional force is given by:
Fk max = μkFN
Where (μk) is the coefficient of kinetic friction and (FN) is the magnitude of the normal force.
<ii> Friction and the Inclined Plane
FN
Ff
Constant Motion
(a = 0)
θ
θ
Fperpindicular
FW
Sin θ = Fparallel
FW
Fparallel = FW Sin θ ⇒ Ff
Fparallel
Cos θ = Fperpindicular
FW
Fperpendicular = FW Cos θ ⇒ FN
AP Physics “B”
Mr. Mirro
Date: ________
Equilibrium, Friction and Newton’s Laws I
Ex 1: A sled is resting on a horizontal patch of snow, and the coefficient of static friction is μs = 0.35.
The sled and its rider have a total mass of 38 kg. What is the magnitude of the maximum
horizontal force that can be applied to the sled before it just begins to move ? [Cutnell4.9]
Ex 2: A skier has just begun descending the 30° slope. Assuming the coefficient of kinetic friction is
μk = 0.10: [Giancoli4.17]
a. Draw a free-body diagram depicting the situation.
b. Determine her acceleration.
c. How fast could she be traveling at four seconds.
Ex 3: Suppose in the previous example that the snow is slushy and the skier moves down the 30° slope at
a constant speed. What could we say about the coefficient of kinetic friction (μk) ? [Giancoli4.18]