Showing posts with label Coefficient of friction. Show all posts
Showing posts with label Coefficient of friction. Show all posts

Friction Problems and Solutions Two

We are solving problems based on the concept friction. It is a force acts opposite to relative motion. Frictional force is directly proportional to normal reaction. Normal reaction is the reaction acting on a body from the surface of contact normal to the surface. The proportionality is eliminated with a proportional constant and it is called coefficient of friction. It depends on the nature of the material and independent of normal reaction, weight of the body and force applied on the body.

Problem 

It is given in the problem that a wooden block of mass M is resting on a horizontal surface and it is pulled with a force making an angle with the horizontal. If coefficient of kinetic friction is given to us, we need to measure the acceleration of the block. The problem is as shown in the diagram below.


Solution

Let the applied force is T and it can be resolved into components. The angle of inclination is given to us and we know the components acting in the horizontal and vertical directions. We know that the weight acts in the downward direction and we can find out the the total force acting in the down ward force acting by the block and the normal reaction is the same value in the opposite direction.

By writing the equation for the resultant force as the difference between the component of the applied force along the direction of motion and the frictional force, we can solve the problem as shown in the diagram below.


Problem

A person is holding a block of mass 2 kilogram between his two hands and he need to keep it with out falling vertically. If the force exerted by each hand is 50 newton, we need to know the coefficient of friction between the surface in contact.


Solution

We know that the applied force by  hands acts like normal reaction and it is twice the applied force as it is applied with both the hands. Thus normal reaction is 100 newton. The weight of the body 20 newton acts in the downward direction and frictional force acts in the upward direction. Thus the product of efficient of friction and normal reaction is equal to the weight of the block acting in the opposite direction. Thus coefficient of friction is 0.2.

Problem

A body of mass 4 kilogram is initially kept at rest on a horizontal surface and coefficient of friction is given to us. A horizontal force is applied on  the body and the distance covered in three seconds is given as 18 meter. We need to measure the ratio of applied force and the frictional force. The problem is as shown in the diagram below.


Solution

As the displacement is given to us, we can use second law of equation of motion and we can find the acceleration and thus the force the acting on the body. As coefficient of friction is also given to us, we can measure the frictional force acting and thus we can also find the effective force generated as shown below. The problem can be further solved as shown here.


Problem

It is given in the problem that under a certain force the body has some acceleration and when force is doubled, its acceleration is different. We need to find the coefficient of friction.


Solution

In each case, we can write the equation for the resultant force and we can equate it to the product of mass of the body and acceleration of each case. They can be further simplified and solved as shown below.


Problem

It is given in the problem that  body is sliding on a horizontal surface and its contact force is double the frictional force. We need to find the coefficient of friction. The problem is as shown below.


Solution

Contact force is nothing but resultant force of normal reaction and fictional force and it can be found using the parallelogram law of vectors. By simplifying it further as shown below, the problem can be solved.

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Friction Problems and Solutions One




Velocity of a Body on Reaching the Bottom of a Rough Inclined Plane









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Friction Problems and Solutions One

Friction is a force that opposes the relative motion between two bodies that are in contact. It is because of molecular force of attraction between among the molecules are in contact. If the two bodies are at rest the friction between them is called static friction and if one is in motion, then it is called kinetic friction. If a body is rolling, it is called rolling friction. To measure the friction,  we need to use coefficient of the friction and it is different for each type of the friction.

Problem

It is given in that a force of 12 newton is acting on a body of mass 4 kilogram and the body is on a rough surface of known coefficient of the friction. We need to measure the acceleration of the body. The problem is as  shown in the diagram below.


Solution

When we apply certain force on a body, it tries to change its position along the direction of the applied force and and hence the frictional force acts in the opposite direction.

We can measure the resultant force as the difference between the applied force and the frictional force. We can measure the acceleration of the system as shown below.

Problem

It is given in the problem that a body of mass 2 kilogram is placed on a horizontal surface and the coefficient of static and kinetic frictions were given. If a horizontal force is applied on a body, we need to measure the frictional force acting on the body. The problem is as shown below.  


Solution

The applied force is only 2.5 newton. Coefficient of static friction is given to us and we can measure the maximum static frictional force as the the product of normal reaction and coefficient of friction. As per the given data, the maximum static frictional force is 10 newton and the applied force is less than that. So the applied force is less than the maximum static frictional force and hence the body continuous in the same state of the rest. The static frictional force self adjusts itself to the applied force. The solution is as shown in the diagram below.


Problem

A train consisting of 30 wagons and each ones mass is given to us. The power of the engine pulling the train is also given to us in the problem. Frictional force per each tonne is given as 12 newton and we need to measure the maximum velocity of the train.


Solution

Total mass of the train is the product of number of wagons and mass of each one. Total frictional force can be found as the product of friction per tonne and the total mass in tonne. We can define power as the rate of change of  work done and the dot product of frictional force and velocity. Using this concept, we can solve the problem as shown in the diagram below.


Problem

A pulling force with a known angle is applied on the body with vertical of block known weight. If the angle of friction is given to us, we need to measure the force required to move the body. The problem is as shown in the diagram below.


Solution

We can understand that the applied force can be resolved into components and one component is helping to move the body and the other turned as the part of the normal reacting. We can write the equation for resultant force and solve the problem as shown below.



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Friction Complete Video Lessons

Friction is a force which opposes relative motion.It is measured basing on the roughness of the surface and it is measured with coefficient of friction. We do know that there is lot of disadvantages because of friction like wear and tear of mechanical parts of machines but without friction we cannot survive.That is why, friction is called necessary is evil. Friction does not opposes motion but it opposes relative motion.

Here in this series of small video lessons, all basic aspects of friction were explained. Each video lesson is short and explains only a specific topic with all the basics required. In general nothing is taken, some thing like basics of the subject is known to some one who is learning from this resource.

Here are the list of topics from the chapter friction.



















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Acceleration of body on rough horizontal surface of accelerating Truck

Body on rough horizontal surface gets locked because of interlocking of irregular surfaces and it generates friction against the relative motion. If the body is on the rough surface of a truck that is accelerating, then the truck behaves like a non  inertial frame with respect to which we shall the study the motion by considering pseudo force. 

It is just because newton laws of motion are not valid in non inertial frame. To apply newton laws of motion to a body in non inertial frame, we shall apply virtual force on the body that is equal to the force on the system but in the opposite direction.

Thus a pseudo force comes into picture in this case. As this pseudo force acts in the back ward direction, the body is tend to move in the back ward direction and hence the frictional force is in the forward direction on the body against the relative motion.

If this pseudo force is less  than limiting frictional force, the block will be in the state of rest and static frictional force self adjusts itself the applied force.

If the truck starts moving with enough acceleration, the block also will have enough virtual force which can dominate the maximum static frictional force and hence the body  starts moving in the back ward direction.

We can measure the effective acceleration of the system using newton laws of motion. Force along the direction of motion shall be treated as positive and force against the motion shall be treated s negative.

Mathematical expression for this friction is derived in the following video lesson as shown below.




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Body on rough and smooth Inclined plane Time of Slide Comparision

When a body of known mass is placed on a inclined plane, the entire weight acts in vertical downward direction. We can resolve that weight into components. One component of weight acts downward along the inclined plane and the other component of weight acts normal to the inclined plane. This second component generates the normal reaction.

If the surface is smooth, there is no frictional force force acts in the system and if the surface is rough, we shall consider the frictional force against the relative motion while we are studying the motion of the body.

We can write the time taken by the body to slide down the inclined plane assuming that it is starting from the state of rest. We can use equation of motion for this derivation.

If there is a relation between the time taken by the body in reaching the bottom of smooth and rough inclined plane, using that relation, we can find coefficient of friction as shown below in the video presented.




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Connected bodies on rough Frictional surface Solving using Newton laws of motion

Connected bodies acceleration and tension between them in the string can be calculated using Newton laws of motion. If one body is on rough horizontal surface, frictional force also has to be taken into consideration. We need to solve this basing on free body diagram and using equations of motion.

Let us consider two bodies of two different masses connected over a light weighted pulley with the help of light strings. As the pulley is friction less, the same tension in the lower string is passed to the string on horizontal surface.

Assuming the force in the downward direction dominates, the system is tend to move in the downward direction and the lower body moves in the downward direction and the upper body on the horizontal rough surface is tend to move from left to right in the system.

We shall apply Newton laws of motion for each body of the system and we shall consider all the forces acting on the body to study its 
motion and never the force applied by the body. Using this concept we can draw free body diagram for each body as shown here in the video. While drawing free body diagram we will consider only forces acting on the body.

 The forces along the direction of motion shall be treated as positive and forces acting against the motion shall be treated as negative while we are writing equation of motion.

As the weight of the hanging body acts in the downward direction,it creates a tightness in the wire and it generates tension in the wire. The same tension is passed to the connected part of the string via friction less pulley.

For the body on the rough horizontal surface, the tension pulls it from left to right and hence frictional force is generated between the rough horizontal surface against the relative motion. We can write equation of motion to this body also as shown.

Solving this two equations of motion, we can get the values of acceleration of the system and tension in the string as shown below.




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Maximum hanging length Chain on Table with out slipping against friction

If a portion of chain is hanging from one face of table, due to its weight it tends to slip from the table. Up to certain length of hanging, it can stay on the table with out slipping.Chain is a body whose mass is uniformly distributed over its length. Mass of the chain is thus directly proportional to the mass of the chain as it is a one dimensional body.

Mass of the chain hanging can be determined as the product of length of the chain and linear density of the chain. Linear density is nothing but mass per unit length of the body. Thus we can identify the mass of the hanging part of the chain as well as mass of the portion of the chain that is lying on the surface of the table.

As some portion of chain is hanging down, its weight acts in downward direction and its it creates a tightness in the chain. This acts like the tension in the chain and in turn in acts on the horizontal portion of the chain that is on the table. This tension tend to slip the chain away from the table and opposite to it, frictional force is generated against the relative motion.

Frictional force here is also the product of coefficient of friction and normal reaction. Portion of the chain on the table applies its weight on the floor of the table and it acts like action. The chain applies reaction on the part of chain on the table and it is nothing but normal reaction. So we can calculate the frictional force acting.

For the chain not to slip, this frictional force has to be balanced by the tension in the chain. Tension in the chain is nothing but the weight of the portion of the chain hanging.

Using this equating forces , we can get the maximum length of chain that can be hung from table with out slipping.The expression is derived in the video as shown below.





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