PES 1110 Fall 2013, Spendier
Lecture 14/Page 1
Today:
- Exam 1 Returned
- Friction (Chapter Section 6.1-6.3)
Friction:
We already know that friction is one of the forces we needed to identify in order to apply
Newton’s Laws of motion:

Friction - f , force which slows a moving object, always opposed to the motion, 180

degree away from velocity) opposite to v .
Friction is a force acting between two touching objects, that acts to oppose any sliding
motion between the two objects.
To understand friction, we use a simplified model of friction that works fairly well for
flat, solid objects in contact with each other. In this model, the amount of friction depends
on the type of materials and whether they objects are in motion (relative to each other).
Demo: pulling a piece of wood along the ground
Piece of wood: mass = 5 kg.
For small forces, the piece of wood will not move. That is because friction cancels with
our pull.


As we increase the pulling force Fp the frictional force f s will also increase until


Fp  f s ,max , when the piece of wood will move.
To keep pulling at a constant velocity we need


F
 x  0 since ax = 0 for constant velocity
net


and the pulling force must equal the frictional force: Fp  f k
PES 1110 Fall 2013, Spendier
Lecture 14/Page 2
Notice that I used different subscripts on friction:

f s …. static friction: Force on a stationary object that keeps it at rest

f s ,max …. maximum static friction: when this is overcome object will move

f k …. Kinetic friction: sliding friction
From the demo we see that once the block is moving we need to apply less force than
right before it moved. Hence, the frictional force is different depending on whether an
object is stationary or moving.
Usually: f s ,max  f k
Mechanism that causes friction:
Surfaces are rough. When two objects are pushed together (for example by gravity) then
these rough surfaces mean that it is hard to slide them past each other
Jagged parts get caught on one another.
The harder these objects are pushed together in the y direction, the harder it is to slide
them in the x direction.
Experiments show that the static friction’s maximum value and the kinetic friction’s
value are approximately constant and obey a simple equation.
f s ,max = μs Fn
(Coefficient of static friction μs multiplied by normal Force Fn)
f k = μk Fn
(Coefficient of kinetic friction μk multiplied by normal Force Fn)
PES 1110 Fall 2013, Spendier
Lecture 14/Page 3
So when normal force is made very small, friction also becomes small.
What is the difference between kinetic and static friction?
Before the object starts moving, it is stuck on the jagged parts and a large push is needed
to overcome these.
Once the object is moving, the jagged edges are moving above one another and are not
getting stuck down in the crags this is why
f s ,max  f k
Because fewer parts are getting stuck once the object is moving.
How can we experimentally measure the coefficients of friction?
Example 1: From our demo we can estimate the coefficient of static friction since we
can measure the force needed to pull the wood with our Newton scale
PES 1110 Fall 2013, Spendier
Lecture 14/Page 4
Example 2: A metal block of 5 kg is placed on a wooden ramp which is initially
horizontal. When the ramp is slowly raised, at what angle will the block begin to slide?
Will the angle depend on the weight of the block? Knowing this angle can we estimate
the constant of static friction?
We see that the expression for the coefficient of static friction is in depend of the weight
of the object.