PH-211 Andres La Rosa

CHAPTER 6: Friction Force ____________________________________________________________________

View of the contact surface at a microscopic scale

Surfaces are rough at microscopic levels

Stationary surface

Moving block

Stationary surface

Then, it turns out, to keep the mass M moving at constant

Here we describe an experimental fact:

velocity, we need to apply a force Fk somewhat smaller than Fs, max

(external force )M

Interpretation of the experimental fact described above:

Stationary surface

Static friction forces

Then, it turns out, to keep the mass M moving at constant

velocity , we need to apply a force Fk somewhat lower than Fs, max

>

Fs, max

Fk

FkFs, max

Maximum static friction force

Kinetic friction force

(external force )

M

What happens when we apply an external force of increasing strength?

M

M

Stationary surface

Stationary surface

Friction force

Magnitude of the friction force

2N

Example

Exercise

If m = 1 Kg then,

N"

m = 1 Kg

mg

N'

N'

N' + N' = mg - 2 Newtons

STATIC CASE

KINETIC CASE

Quantifying the friction force

=

=

Exercise μs = 0.15

CH-6, Problem #25

B

A

What is the maximum weight of block-A, for which the system will remain stationary? (Block-B weights 711 N)

No horizontal motion implies

Maximum static friction force

No motion along the vertical direction implies,

WB= 711 N

μ = 0.25

fs, max

=

=

=

= Newtons = 178 Newtons

fs, max

Warm up, for problems involving inclined planes 1)

Resolving the force mg into components parallel and perpendicular to the ramp

2)

3)

4)

5)

Ff

Ff

Ch-6 Problem 79. Block A in Fig. 6-56 has mass mA 4.0 kg, and

block B has mass mB 2.0 kg. The coefficient of kinetic friction

between block B and the horizontal plane is �k 0.50. The inclined

plane is frictionless and at angle � 30°. The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration of the blocks.

Is a1 =a2?

a1

a2 2 Kg4 Kg

Forces on m1 Forces on m2

Example. A block is placed on an inclined plane

Question: Is ?

a) First, let's consider no other external force than the gravitational force

m g sin θ =

b) Let's apply now an external force Fext

v = 0 v � 0

2. Usually μs > μk

0.1 < μ <1 for many pair of materials

v = 0 v

However: μ depends very much on surface conditions (cleanliness)

This rule is true only if the objects in contact do not deform appreciable.

1. The friction force is proportional to the normal force at the surface: f = μs N

N1

N2

f1 f2

General rules for dry sliding friction

3. For a given object, the friction force is independent of the apparent area in contact with the supporting surface

In both cases the same force F is needed to drag the block.

apparent areaa

Explanation: The actual contact area is the same in both cases (since the normal force is the same)

actual contact area

Increasing the load increases the normal force N, and increases the actual contact area

fs, max α actual contact area Actual contact area α N Hence fs, max α N More quantitatively, fs, max = μ N

Key aspects in friction: - The actual contact area is proportional to the normal force - When two objects are forced together, the high peaks of their surface will crumble, bringing more and more area into intimate contact.

Metal-metal friction