Mu of the Shoe

Chapter 2, Activity 6

Friction• What is friction?

– An interaction between a moving object and its environment• Produces heat and loss of energy• Slows things down

– Water viscosity– Air Air resistance

Friction• What is friction?

– Between two surfaces, they may or may not be in motion relative to one another.• If they are in motion relative to one

another, it is kinetic friction.• If the two objects do not move relative to

one another, it is static friction

Friction• Braking friction

What do you think?• Why do some sports require special

shoes?– Shoe companies have done large

amounts of research and development on the materials and design of shoes to enhance their performance.

– Many of the design characteristics are to maximize the friction between the sole of the shoe and the surface it is intended to be used on.

Friction• How does friction affect the motion

of objects?– It can slow an object down like the

friction between the tires and the road.– Friction is responsible for increasing

the speed of an object like a car.– Friction is also responsible for objects

being able to change direction.

Static Friction

System

FforwardFfriction

Fground-on-crate

Fgravity

FforwardFfriction

Fnet = Fforward – Ffriction

Since the crate is not accelerating, Fnet = 0

Fforward = Ffriction

If the crate is not moving, then the pushing force will equal the frictional forceFforward = Ffriction

• Static Friction:– The resistive force that keeps an object

from moving.

Kinetic Friction

System

FforwardFfriction

Fground-on-crate

Fgravity

• Kinetic Friction:– The resistive force that opposes the relative

motion of two contacting surfaces that are moving past one another.

FforwardFfriction

Fnet = Fforward – Ffriction

Fnet

If the crate is moving at a constant speed, then the pushing force will equal the frictional force

Fforward = Ffriction

Determining the Frictional Force

• The force of friction is proportional to the normal force and a proportionality constant (µ - pronounced mu) called the coefficient of friction.

• For static friction:– 0 < Ff, static < µsFN

• For kinetic friction:– Ff, kinetic = µkFN

• Note: FN = the force normal (perpendicular) to the frictional force on the object.

• µ is dimensionless• Note: Ff, static > Ff, kinetic (You have

experienced this!)

The Normal Force• The normal force is a force that

opposes the Earth’s gravitational attraction and is perpendicular to the surface that an object rests or is moving on.– For a horizontal surface, FN = Fg = mg.– In other words, the normal

force equals the weight.FN

Fg

1. The formula for friction is similar to those we have already used where there are three variables:

Ff = µFN

– As just mentioned, for a horizontal surface, the normal force is the same as the weight of the object (Fg = mg)• m = mass in kilograms• g = acceleration due to gravity (10 m/s2)

Ff

µ FN

The Math of Friction

Determining the Mu of the Shoe

1. Determine the mass of the shoe in kg.2. Determine the normal force, which will be the same

as the gravitational force of the shoe (Fg = mg), where g = 10 m/s2.

3. Determine the tensional force in the spring scale while pulling the shoe at “constant speed.” Under these conditions, the tensional force will equal the frictional force.

4. Find µ:

FTFf

Fg

FNµ = Ff/FN = FT/Fg

Example 1: Determining Friction

• Assume that the man in the figure is pushing a 25 kg wooden crate across a wooden floor at a constant speed of 1 m/s.

– How much force is exerted on the crate?

System

FforwardFf

FN

Fg

Diagram the Problem

System

FforwardFf

FN

Fg

FforwardFf

FN

Fg

y-direction: Normal force equals gravitational force (FN = Fg)

x-direction: Fnet = Fforward - Ff Since the crate is moving with constant speed, a = 0, Fnet = 0, and Fforward = Ff

+y

+x

State the Known and Unknowns• What is known?

o Mass (m) = 25 kgo Speed = 1 m/so Acceleration (a) = 0 m/s2

k = 0.2 (wood on wood - found in reference table)

• What is not known?o Fforward = ?

Perform Calculations• y-direction:

oFg = FN = mg• x-direction: a = 0

oFnet = Fforward – Ffo Fforward = Ffo Fforward = kFN; Fforward = kmgo Fforward = (0.2)(25 kg)(9.8 m/s2)o Fforward = 49 N

0

Key Ideas• Friction is an opposing force that

exists between two bodies.• Friction is proportional to the normal

force and the coefficient of friction; static or kinetic.

• The force required to overcome static friction is greater than that required to overcome kinetic friction.