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Friction and Elements of Rigid Body Dynamics

1 Friction 1.1 Explanation 2 Types of Friction 2.1 Static Friction 2.2 Dynamic Friction 3 Limiting Friction 4 Normal Reaction 5 Co Efficient of Friction 6 Laws of Friction 6.1 Laws of Static Friction 6.2 Laws of Dynamic Friction

FRICTION AND ELEMENTS OF RIGID BODY DYNAMICS

1 Friction

1.1 Explanation

2 Types of Friction

2.1 Static Friction

2.2 Dynamic Friction

3 Limiting Friction

4 Normal Reaction

5 Co Efficient of Friction

6 Laws of Friction

6.1 Laws of Static Friction

6.2 Laws of Dynamic Friction

1 Friction

A force which prevents the motion or movement of the body is called friction or force of friction and its direction is opposite to the applied external force or motion of the body. Friction is a force of resistance acting on a body which prevents or retards motion of the body. Or When a body slides upon another body, the property due to which the motion of one relative to the other is retarded is called friction. This force always acts tangent to the surface at points of contact with other body and is directed opposite to the motion of the body.

1.1 Explanation The other end of the string is connected to the spring balance. Apply an external force on the balance. Gradually increase the magnitude of the external force. Initially the body will not move and the effect of the applied force is nullified. This is because there acts a force on the block which opposes the motion or movement of the block. The nature of this opposing force is called friction. It depends upon many factors. The major cause of friction is the microscopic roughness of the contact surfaces. No surface is perfectly smooth. Every surface is composed of crests and falls as shown in fig b. It is the interlockingof the crests of one surface into the falls of the other surface which produces the resistance against the movement of one body over the other body. When the force exerted is sufficient to overcome the friction, the movement ensures and the crests are being sheared off. This gives rise to heat and raises the local temperature. This is also the reason of the wear of the contact surfaces. This phenomenon of friction necessitates the presence o fluid film between the two surfaces to avoid wear of surfaces. The process of creating the fluid film is called lubrication

2 Types of Friction

Friction is of the following two types.

5.2.1 Static Friction

It is the friction acting on the body when the body is at the state of rest or the friction called into play before the body tends to move on the surface is called static friction. The magnitude of the static friction is equal to the applied force. It varies from zero to maximum until the movement ensures.

2.2 Dynamic Friction

It is the friction acting on the body when body is in motion is called dynamic friction. Dynamic friction is also known as kinetic friction. The magnitude of the dynamic friction is constant.

The dynamic friction has two types

i.                   Sliding Friction

ii.                   ii. Rolling Friction

i. Sliding friction

The sliding friction acts on those bodies, which slide over each other for example the friction between piston, and cylinder will slide friction because the motion of the motion of the piston in cylinder is sliding and there is surface contact between piston and cylinder.

ii. Rolling Friction

The rolling friction acts on those bodies which have point contact with each other for example the motion of the wheel on the railway track is the example of rolling motion and the friction between the wheel and railway track is rolling friction. It is experimentally found that the magnitude of the sliding friction is more than the rolling friction because

in the rolling friction there is a point contact rather than surface contact.

3 Limiting Friction

The maximum friction (before the movement of body) which can be produced by the surfaces in contact is known as limiting friction .It is experimentally found that friction directly varies as the applied force until the movement produces in the body. Let us try to slide a body of weight w over another body by a force P as shown in fig

A little consideration will show that the body will not move because the friction F which prevents the motion. It shows that the applied force P is exactly balanced by the force of friction acting in the opposite direction of applied force P. if we increase the force P by increasing the weight in the pan, the friction F will adjust itself according to applied force P and the body will not move. Thus the force of friction has a property of adjusting its magnitude to become exactly equal and opposite to the applied force which tends to produce the motion.There is however a limit beyond which the friction cannot increase. If the applied force increases this limit the force of friction cannot balance applied force and body begins to move in the direction of applied force. This maximum value of friction, which acts on body just begin to move, is known as limiting friction. It may be noted that when the applied force is less than the limiting friction the body remains at rest, and the friction is called static friction, which may have any values zero to limiting friction.

4 Normal Reaction

Let us consider a body A of weight “W” rest over another surface B and a force P acting on the body to slide the body on the surface B as shown in fig A little concentration will show that the body A presses the surface B downward equal to weight of the body and in reaction surface B lift the body in upward direction of the same magnitude but in opposite direction therefore the body in equilibrium this upward reaction is termed as normal reaction and it is denoted by R or N.

Note

It is noted the weight W is not always perpendicular to the surface of contact and hence normal reaction R is not equal to the weight W of body in such a case the normal reaction is equal to the component of weight perpendicular to surface.

5 Co Efficient of Friction

The ratio of limiting friction and normal reaction is called coefficient of friction and is denoted by μ.

Let R = normal reaction

And F = force of friction (limiting friction)

μ = Co efficient of friction F/R = μ

F = μ R

6 Laws of Friction

These laws are listed below:

6.1 Laws of Static Friction

The force of friction always acts in a direction opposite to that in which the body tends to move.

·        The magnitude of force of static friction is just sufficient to prevent a body from moving and it is equal to the applied force.

·        The force of static friction does not depend upon, shape, area, volume, size etc. as long as normal reaction remains the same.

·        The limiting force of friction bears a constant ratio to normal reaction and this constant ratio is called coefficient of static friction.

6.2 Laws of Dynamic Friction

·        When a body is moving with certain velocity, it is opposed by a force called force of dynamic friction.

·        The force of dynamic friction comes into play during the motion of the body and as soon as the body stops, the force of friction disappears.

·        The force of dynamic friction is independent of area, volume, shape, size etc. of the body so long the normal reaction remains the same. However, to some extent it varies with the magnitude of

·        velocity of the body. Force of dynamic friction is high for low speeds and low for very high speeds.

·        The ratio of force of dynamic friction and normal reaction on the body is called coefficient of dynamic friction.

Example 1: A horse exerts a pull of 3 KN just to move a carriage having a mass of 800 kg. Determine the co efficient of friction between the wheel and the ground. Take g = 10 m/sec²

Given P = 3 KN Mass = m = 800 Kg g = 10 m/sec²

Required co efficient of friction = μ =?

Working formula F = μ R

Solution we know that W = mg

W = 800 x 10 = 8000 N A little consideration will show that the weight of the carriage is equal to the normal reaction because that the body is horizontal to the plane as shown in fig

Therefore W = R and P = F

put the values in working formula we get

300 = μ 8000 μ =0.375

Result co efficient of friction = 0.375

Example 2: A pull of 490 N inclined at 30º to the horizontal is necessary to move a block of wood on a horizontal table. If the coefficient of friction between to bodies in contact is 0.2 what is the mass of the block.

Given P = 490 N θ = 30º μ = 0.2

Required mass of block =?

Solution

Now consider the following diagram and also resolve the force P into horizontal and vertical components. F = μ R w = mg

Now apply the condition of equilibrium the forces acting in x axis is positive

Σ Fx = 0

P Cosine θ – F = 0

P Cosine θ – μ R = 0

490 Cosine 30– 0.2 x R = 0 Therefore

R = 2121.762

Now consider the forces acting in y axis is positive

Σ Fy= 0

R + P Sine θ – W = 0 R + P Sine θ – mg = 0

2121.762 + 490 Sine 30– m x 9.81 = 0

m = 241.260 Kg

Result mass of the wooden block = 241.260 Kg

Example 3: A body of mass 100 Kg rests on horizontal plane the co efficient of friction between body and the plane 0.40. Find the work done in moving the body through a distance of 20 m along the plane.

Given m = 100 Kg μ = 0.40 d = 20 m

Required work done =?

Working formula 1 W = F x d

2 Fs = μ R

Solution we know that R = W = mg R = W = 10 x 9.81 = 98.1 N

Put the values in 2nd working formula we get Fs = 0.40 x 98.1

Fs = 39.24 N

Now put the values in 1st working formula W = 39.24 x 20

W = 748.8 N

Resultant weight = 748.8 N

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