# Table Without Friction: Various Solved Problems

The force which opposes the motion of a body is known as a frictional force.

However, a table without friction is not exactly possible. But we can be very close to the table without friction by having a smooth, flats surface and using lubricants.

## Pulley on a table without friction

A pulley on a table without friction means that a friction-less pulley on the table has negligible or, say, no friction in it, and it is free to rotate without any resistance.

Let’s go through a problem to see a pulley without friction:-

## Q. A block had A of mass m₁ = 800 kg lies on a horizontal table. A light string connected to the block passes over a friction-less pulley, and to its other end, another block R of mass m2 = 12 kg is fastened. The coefficient of kinetic friction between the block and the table is mu k =0.08. T1 block A is sliding on the table. Calculate the acceleration of each block. Take g=10.

In the given figure, the forces exerted by each block are shown.

Here the block B exerts a force of T on block A.

Through the tension in the string. The Block A exerts an equal reactionary force on B through the same tension T in the string.

In addition to the tension T, the other forces on block A, are gravity force mg on the block, normal reaction R, and the kinetic frictional force fk. If a be the acceleration in the block in the horizontal direction, then by Newton’s second law (net horizontal force = mass x acceleration),

T-fk=m1a

But, fkkR=μkm1g (as there is no motion in vertical direction.)

T-μkm1g =m1a

So we got to know that the net vertical force will be m2g-T on block B. And acceleration is a.

m2g-T=m2a

On substituting values we get,

m2g-μkm1g-m1=m2a

a=(m2km1g)/(m1+m2)

On putting the values of each, we will get:-

## Q. A particle of mass 2 gm performs oscillatory motion. The motion is performed on the concave side of a spherical utensil, whose radius is 4meter. Suppose the body’s motion starts from a point on the dish at a height 2 cm from the horizontal plane. The which is coefficient of friction is 0.02. They calculate the total distance covered by the particle before it comes to rest.

Ans. We know that the potential energy of the particle is given as U=m g h. Where the normal reaction force of the surface of the dish on the body, when it is at the bottom, is given as:-

R=mg.

Here the kinetic friction between the particle and the surface dish is fkkR=μkmg.

The work done by the particle before coming to rest given as, W=fk*d=μkmgd

Now, the body’s potential energy will be exhausted when doing work against friction. Thus,

mgh=μkmgd

d=h/μk=1cm/0.01=100cm

## Q. A surface, which has a frictionless surface. Give the reason why we cannot jump off from the surface?

We cannot jump off from a horizontal surface that does not have any friction. This happens because the surface will not provide any normal reaction force.

## Q. A block b is at rest. On block b, whose mass is 5kg, a block a is placed whose mass is 4 kg upon it. If we apply a force of 12newton, then block a will slide on block b. find the horizontal force to be applied on block b so that both block a and b combined move together.

Suppose the mass of blocks A and B be m1 and m2 .here the coefficient of kinetic friction between the two-block blocks is given as, uk, so now the frictional force applied between the will be:-

fkkR=μkm1g

When a force of 12N is applied, block A moves on block B.

We know that block B is on a smooth surface. So if we want to move to block a and b together, then the force applied on block B should be equal to the frictional force applied on A by B and applied on B by A.

By the obtained force, both blocks will move if applied to the block.

Here the acceleration will be:-

a=F/(m1+m2)=27N/(4kg+5kg)=3N/kg=3m/s2

## Q. Give three ways through which friction can be reduced. Explain?

As we know, friction can be eliminated, but we can reduce it through following ways:-

### Lubrication:-

The irregularities present in molecules are the reason behind friction.

If we polish the surface, and the surface between the objects in contact, then the irregularities are filled by the polish material. This polishing decreases the friction as all interlocking decreases. And the object starts moving smoothly.

### Friction also depends upon material:-

The friction exerted between two objects also depends upon the material of the two. So if we use materials whose coefficient of friction is low, they will exert less friction. For example, the vehicle tires are made of rubber as friction between rubber and concrete is less.

### Ball bearings:-

Ball bearings consist of two concentric cylinders. Between them, numerous spherical balls are present.

The axle of the vehicle of the machine in which it is fitted is attached to its inner cylinder. And the wheels are put on the outer cylinder. When the axle of the vehicle or machine rotates clockwise, the ball bearings present with the outer cylinder move anticlockwise—this causes rolling motion. Here, instead of sliding on each other, the two cylinders are in a rolling motion. So the sliding friction is converted to more negligible rolling friction.

Riya Pandey

I am Riya Pandey. I have completed Post Graduation in physics in 2021. Currently I am working as a Subject Matter Expert in Physics for Lambdageeks. I try to explain Physics subject easily understandable in simple way.