Lecture 8 Friction&Drag

8/3/2019 Lecture 8 Friction&Drag

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Example 5:

F

m1

m2

m1=12kg

m2=3kg

F=45N

Find the tension in the rope

connecting the two masses

Find the acceleration of the

two masses



Friction

Friction is a result of contact between dry solid surfaces.

Even though friction is considered as a restricting force

and a waist of energy, such as in car engine..

In many other cases it is very important.

For example:

1) Motion of a wheel

2) Walking

3) Tying knots4) Holding things

5) And much more



What is the source of friction?

Friction is the sum of all the forces acting between thesurface atoms of one body and the surface atoms of

another body.

Therefore the better the contact is the larger the friction.

Remember: No surface is perfect.



How do we “see” friction?

1) If we send an object sliding

horizontally across a table it

slows down.

v2) In order to move and object

on a smooth surface with

constant velocity we have toconstantly apply a force.

v



Exploring friction

Friction, f = 0F N

mg F N

mg

F

If object is not moving, f = F

F N

mg

2F If object is still not moving, f = 2F

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Exploring fr iction (continue)

F N

mg

F f

The direction of f is to the left

F N

mg

F f

The direction of f is to the right

Friction is always opposing the applied force








What happens during motion?

Once the object starts moving we usually feel a relief.This is because the friction force opposing the motion

is reduced.

The friction between sliding surfaces is less than

between static surfaces.

f s > f k

Summary:

F (applied)

f

f s,max

f k

Start of motion



What determines f s and f k ?

F

F f

Will f increase when we add

the mass on top?

F f

Will f increase when we push

the object down without

increasing the mass?

The force that is changing in both cases is F N .

Conclusion f is proportional to F N .

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The friction is also dependent on the interaction

between the two surfaces involved.

That determines the coefficient of proportionality

between f and F N .

N F f

N s s F f max,

Finally:

But since, the static friction is different than

the kinetic friction it implies that the coefficientis different.

N k k F f



Conceptual Question 1:

A block of mass 10 kg lies on the floor.What is the magnitude of the frictional force acting

on it from the floor?

A)98 N

B)0 N

C)50 N

D)49 N




If a horizontal force of 50 N is now applied to the blockbut the block does not move.

What is the magnitude of the frictional force on it?

A)98 N

B)0 N

C)50 N

D)49 N




If the maximal static frictional force f s,max is 100 N.Will the block move if we push it with a horizontal force

of 98 N?

A)Yes

B)No




If the maximal static frictional force fs,max is 100 N.What will be the magnitude of the frictional force on the

block if we push it with a horizontal force of 98 N?

A)100 N

B)49 N

C)98 N

D)2 N



Numerical Example:

A truck is trying to unload its

cargo by lifting its container in

an angle.

At what angle will the cargo

start sliding down assuming it’sa one mass m and that the

coefficient of static friction

between the cargo and the floor

of the container is µ s ?



Drag Force

The “Drag Force” is caused by a FLUID.

Fluid is anything that can flow (gas, liquid).

The Direction of the drag, as friction, always

against the direction of the motion.

v D



What does Drag depend on?

Fluid density

Effective cross-sectional Area of the object A

The velocity of the object v



Dimensional Analysis

t L

time Lengthv

L Area A

L

M

volume

mass

2

3

22

t

LM

time

Lengthmass Force D

2v A D



2

2

1

AvC D

Finally:

C is called the “DRAG COEFFICIENT”

and it is determined experimentally.

Typical values range 0.4 – 1.0



Question:

What happens to an object which is dropped from avery high building if we consider the drag force?

Remember: the drag force increases with the velocity

It reaches a maximum velocity called

“Terminal Velocity” given by:

AC

F vt

2



Example

Calculate the magnitude of the drag force on a missile53cm in diameter cruising at a 250m/s at low altitude,

where the air density is 1.2kg/m3, assuming C=0.75.

What will the propelling force of the missile have to be?

d v

DF p




If an object that is being dragged by a force F through air has a terminal velocity v.

What will be its terminal velocity if we drag it with the

same force through another gas of density ¼ that of

air?

A)¼ v

B)½ v

C)2 v

D)4 v

Lecture 8 Friction&Drag

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