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FORCES OF FRICTION--More Newton's Laws
INTRODUCTION: Frictional forces act to oppose
relative motion between surfaces that are in contact.
Frictional forces act parallel to the surfaces.
STATIC FRICTION: Static friction occurs between
surfaces at rest relative to each other. The
MAXIMUM force of static friction is the smallest force
necessary to start motion. Rolling friction (not
skidding) is also a form of Static Friction.
KINETIC FRICTION: Once motion starts, a smaller
force is necessary to keep this motion going at a
uniform rate. This frictional force acting between
surfaces in relative motion is known as Kinetic Friction.
It is also known as sliding friction (skidding is an
example).
COEFFICIENTS OF FRICTION: The frictional force
between two surfaces depends upon the Normal
force and the nature of the surfaces in contact.
To find the normal force, and the friction, you must
first draw a "Free Body Diagram", or "FBD".
USING THE FREE BODY DIAGRAM.
A large number of problems involving actual structures
can often be reduced to a problem concerned with a
particle. This is done by choosing a particle, and
drawing a separate diagram showing this particle and
the forces acting on it. This diagram is known as a
Free Body Diagram. It is a simplified diagram showing
the forces acting on an object in a "schematic" form.
Newton's Second Law of Motion forms the basis for
our friction applications.
REMEMBER:
Force = mass times acceleration
or F = ma
The Force is also a vector quantity.
We write this as:
∑F=ma
"The sum of the forces equals mass times accel.
Use the following description to try to draw an FBD:
Given a block of mass 10 kg on a level surface, if the
block just starts moving a when a force of 50N is
applied to push it , what is the coefficient of Static
Friction?
Don't try to solve this, just make a diagram.
Forces on diagram:
value is usually provided in tables.
This coefficient must be specified as μ s
or μ k
, the
static and kinetic coefficients. Typically μ s
is greater
than μ k
, but for low friction surfaces they can be
equal.
The force of friction is always pointed opposite to the
direction of motion.
EXAMPLE 1: Block on a plane surface.
Given a block of mass 10 kg, if the block just starts
moving a when a force of 50N is applied , what is the
coefficient of Static Friction?
FIRST, draw a diagram showing applied force, Friction
force, weight, and the Normalforce.
The Normal force, by definition, is always perpendicular
to the surface it is touching.
SECOND: Analyze the drawing. As you can see, the
only forces acting in the "y" direction are N and mg, so
they must be equal to each other.
Thus: N=mg = 10kg x 9.8 =98 Newtons
Since the only forces in the x direction are F and F f
they must be equal.
Thus: F=F f
= 50 Newtons (given)
so F f
= μ s
N=50 Newtons,
so μ s
= F
f
/ N
μ s
μ s
Example 2: A 2000kg car is moving at 24 m/s. What
is the shortest distance to brake to a halt? μ s
You need to find the deceleration. Remember that
F=ma. If you can find F, you can solve for a.
The Force you can apply is just the force of friction.
F
f
= μ s
N
There is no pushing force, since you don't hit the gas
and the brakes at the same time!
Draw the FBD:
Example 3: How much force is needed to keep a
3000Newton car moving on a level road. Use μ = .04.
Force is equal to the force of friction.
The Normal Force is just the weight, 3000 Newtons
Thus, F f
= μ s
N = .04 x 3000Newt=120Newtons
Example 4: A force of 200N is just enough to start a
50kg trunk moving. Find the coefficient of static
friction.
Force is equal to the force of friction.
The Normal Force is just the weight, 50 kg x 9.8= 490
newt Thus, F f
/N = μ s
= 200/490 μ s
Example 5: Suppose the above trunk can be kept
moving with just a force of 100N. What is the
coefficient of Kinetic Friction?
The Normal Force is just the weight, 50 kg x 9.8= 490
newt Thus, F f
/N = μ k
= 100/490 μ k
