Download Unit 5: Applications of Newton`s Laws

Unit 6:
Applications of Newton’s Laws
Sections A and B: Friction

Corresponding Book Sections:
– 6.1

PA Assessment Anchors:
– S11.C.3.1
What’s different now?

In the last unit, we didn’t account for a
very important force:
– Friction
• The resistance exerted on an object while it’s in
motion
Kinetic Friction

The friction encountered when surfaces
slide against each other with some
speed

Symbol: fk
So, how does friction affect
different objects?
The object with
twice the mass
has twice the
friction acting
on it.
But why…?
Kinetic Friction, derived…

Kinetic friction is proportional to the
Normal Force.
fk = µkN
Force of kinetic friction = Coefficient of kinetic friction x Normal
force
(Pronounced “Mew”)
Coefficient of Kinetic Friction

As this increases, so does the force of
friction between two objects.
Basic facts about Kinetic Friction
1. Proportional to the Normal Force
fk = µkN
2. Does not depend on speed of the
objects
3. Does not depend on area of contact
between the surfaces
Practice Problem #1

Refer to Example 6-1
FBD for Example 6-1
Static Friction

The friction that tends to keep two
objects from moving relative to each
other

This is usually stronger than kinetic
friction because surfaces can form a
stronger connection
Static Friction, cont…
fs, max = µsN
Maximum static force of friction = Coefficient of static friction x Normal forc
The maximum static frictional force will
occur immediately before the object starts
moving. This is when kinetic friction will take
over.
Changing from Static to Kinetic
No Applied Force
Small Applied Force
Big Applied Force
Largest Applied Force
Kinetic Friction
Takes Over
Basic facts about Static Friction
1. Can be any value between 0 and
fs, max = µsN
2. Does not depend on area of contact
between the surfaces
3. Is parallel to contact surface and in
direction opposite that of motion
Practice Problem #1

Refer to Example 6-3, Page 143
FBD For Practice Problem #1
Is the friction between a car’s
tires and the roads kinetic and
static?

Think about how you walk

With each step, your foot is in contact
with the ground (static friction)

This is what your car is doing really
really quickly
A picture to help explain…
Skidding vs. Braking

Why are anti-lock brakes desirable?
– When a car skids, the friction acting on it is
kinetic
– When a car brakes (wheels still rolling), the
friction acting on it is static
A picture to explain…
Section C: Tension

Corresponding Book Sections:
– 6.2, 6.3, 6.4

PA Assessment Anchors:
– S11.C.3.1
Tension

The force on a string that would be
required to hold the string together if it
was cut at any point
Practice Problem #1

What is the tension force required to
hold a 50 kg object motionless above
the ground?
Practice Problem #2

How much tension force is needed to
pull a 10 kg object with an acceleration
of 3.5 m/s2 if the coefficient of kinetic
friction is 0.4?
Practice Problem #3

Refer to Example 6-4, Page 147
FBD for Example 6-4
Section D: Springs

Corresponding Book Sections:
– 6.2

PA Assessment Anchors:
– S11.C.3.1
Hooke’s Law

A spring stretched or compressed by
the amount x from its equilibrium exerts
a force given by:

F = - kx

k = force constant or spring constant
– Units: N/m
Generally Speaking…

If a spring is compressed:
F = -kx
• This makes “x” negative

If a spring is stretched:
F = kx
• This makes “x” positive
Practice Problem #1

A 1.5 kg object hangs motionless from a
spring with force constant of k = 250
N/m. How far is the spring stretched?
Practice Problem #2

What amount of spring force is needed
to pull a 40 kg object with constant
speed if the coefficient of kinetic friction
is 0.25?
Section E: Centripetal Motion

Corresponding Book Sections:
– 6.5

PA Assessment Anchors:
– S11.C.3.1
What is centripetal motion?

Centripetal
Acceleration
– A “center directed”
acceleration

Motion where the
direction of the
velocity changes
continuously
How do we find centripetal
acceleration?

Direction is towards center of circle

Equation:
2
v
acp 
r
velocity
centripetal acc. =
radius
2
How do we find the centripetal
force?

Directed toward center of circle
2
v
Fc  m
r
velocity
centripetal force = mass *
radius
2
Practice Problem #1

Refer to Example 6-8 on page 159
Practice Problem #2

Refer to Example 6-9 on page 161