Friction experiment

For different values of M1 vary the mass of M2 until the block moves.

Wood-Table Mirror-Table

M1 M2 μ M1 M2 μ

Average value of μ Average value of μ

. Vertically:

1

0R W

R M g

Horizontally (At the point of sliding):

2 1

2

1

0P Fr

P R

M g M g

M

M

Ideas for

teaching

Friction

Sue de Pomerai

Warm up

Two people push against each other. Who

moves?

As above but one person on wheels/ice

skates?

Types of force at A level

1. Every object continues in a state of rest

or uniform motion in a straight line

unless acted on by a resultant external

force.

2. Resultant force = mass × acceleration

or F = ma

3. When one object exerts a force on

another there is always a reaction

which is equal and opposite in

direction to the acting force.

Newton’s Laws

What is friction? • Friction is a resistance force

• It opposes the relative motion of surfaces in contact

• For a stationary object, any frictional force is always at

exactly the correct size and direction to keep the object

stationary.

• Frictional force has a maximum value, when the

resultant force on an object exceeds this maximum, the

object will move.

• The model of friction we use assumes that whilst and

object is moving, the frictional force is constant at this

maximum value.

• A frictional forces

oppose motion.

• The magnitude

depends on the

surfaces in contact.

• It will have a

maximum value.

Fr ≤ μ R

A model for friction

Example coefficients of friction

Surfaces μ

Ice Steel 0.03

Wood - waxed Dry snow 0.04

Wood - waxed Wet snow 0.1

Tire, wet Road, wet 0.2

Car tire Grass 0.35

Wood Brick 0.6

Skin Metals 0.9

Tire, dry Road, dry 1

Rubber Rubber 1.16

Platinum Platinum 1.2

Mathematical Modelling A car at an accident skids down a gentle slope

leaving a skid mark of 20m before it collides with a

stationary vehicle.

• How fast was the car travelling when it began to

skid?

• Was it breaking the 30mph speed limit?

Formulating a model The first step is to draw up a feature list to include

all those factors that might affect the solution of the

problem.

• The road and tyre conditions.

• The gradient of the slope.

• The speed of impact between the two cars.

• The conditions of the road.

Simplifying assumptions • The road is horizontal.

• The car is to be modelled as a particle.

• The speed of impact is zero.

• There is constant friction force and no air

resistance.

• The coefficient of friction between the tyres and

the road is known (let’s say 0.8)

The mathematical problem A car at an accident skids down a gentle slope leaving a

skid mark of 20m before it collides with a stationary vehicle.

• How fast was the car travelling when it began to skid?

• Was it breaking the 30mph speed limit?

A car skids 20m to rest on a horizontal road. If the

coefficient of friction is 0.8 find the initial speed of

the car.

Experiment For different values of M1 vary the mass of M2 until

the block moves.

The mass of block is 160g

• Put the block on the

table

• Tip the table till the

block just starts to

slide

• Measure the angle of

the table

Confirming your result

R

W

Fr

Theory Resolving parallel and

perpendicular to the plane:

Perpendicular:

Parallel:

At the point of sliding Fr = μR

R W cos 0

R W cos

W sin Fr 0

W W cos

sin

cos

tan

Resolving and equilibrium

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Teaching Mechanics © MEI 2016

Mathematical Modelling – Skidding Motorbike Problem Statement A car at an accident skids down a gentle slope leaving a skid mark of 20m before it collides with a stationary vehicle. How fast was the car travelling when it began to skid and was it breaking the 30mph speed limit? Formulation The first step is to draw up a feature list to include all those factors that might affect the solution of the problem. The list below includes a number of important factors. The road and tyre conditions. The gradient of the slope. The speed of impact between the two cars. The conditions of the road. Were all the wheels locked? Are there any further factors that you think should be included? The assumptions below allow a simple model to be formulated so that a mathematical problem can be defined. The road is horizontal. The speed of impact is zero. There is constant friction force and no air resistance. The coefficient of friction between the tyres and the road is 0.8. The car is to be

modelled as a particle. Mathematical Problem A car skids 20m to rest on a horizontal road. If the coefficient of friction is 0.8 find the initial speed of the car.

Teaching Mechanics © MEI 2016

Mathematical Solution As the car is skidding the friction force

will take its limiting value of R .

So,

mmgF 108.0

where m is the mass of the car and g is taken as 10 ms-2. The acceleration of the car is given by

2-ms 8

8

m

m

m

Fa .

Now the speed can be found using

asuv 222

1-

2

22

ms 9.17

320

20)8(20

u

u

u

Interpretation The initial speed predicted can be converted to give 40mph. This figure clearly suggests that the car was breaking the speed limit. Compare with Realitv The Highway Code provides a useful source of data that can be used to compare the results with reality. The Highway Code quotes a distance of 80 feet or 24m as the braking distance for 40mph. This compares favourably with the prediction made above. Criticism of the Model The two major criticisms that can be made of this model are that the road is not horizontal and that the speed of impact is not taken into account.

R=mg

mg

F

v

Teaching Mechanics © MEI 2016

Reformulation The diagram shows the forces acting when the road is assumed to be at an angle of 5 to the horizontal. The normal reaction now has the magnitude,

5cosmgR

and the resultant force up the slope on the car is,

So the acceleration is

2-ms 96.6

)5sin5cos8.0(8.9

)5sin5cos(

ga

Using this value for a with an impact speed of zero gives.

mph 37or ms 7.16

4.278

20)96.6(20

1-

2

22

u

u

u

Notice that taking account of the hill reduces the initial speed As a final refinement to the model an impact speed 9 ms-l or approximately 20 mph could be introduced. There was only minor damage to the vehicles which suggests that such a value is reasonable. Using this gives a revised initial speed

mph 42or ms 0.19

4.359

20)96.6(29

1-

2

22

u

u

u

It is interesting to note how close the two revised estimates are to the original prediction and that the conclusion that the car was breaking the speed limit was confirmed by both revisions.

R

F

mg 5

cos5 sin5 ( cos5 sin5 )mg mg mg