## Saturday, November 12, 2016

### Laws of Motion Problems with Solutions Six

Newton Laws of motion deals with the impact of force on the motion of the body. This force can be defined as the rate of change of momentum. Here in this post we are going to discuss regarding connected bodies. The bodies are connected with the help of string or in contact with each other. The string becomes tight and there is a force is generated in the sting and it is called tension.

Problem

It is given in the problem that two masses of 10 and 20 kilogram are connected by a mass less spring. A force of 200 newton acts on 20 kilogram mass and at a certain instant acceleration of the other body is given. We need to find the acceleration of the other body. The problem is as shown in the diagram below.

Solution

The spring connected between the bodies as if like a string and a tension is generated in it when the force is applied on the connected mass. On 10 kilogram mass only force acting is the tension in the string. On the 20 kilogram mass, applied force is acting on the it towards right and tension acts in opposite direction. Thus we an write equation of motion and solve the problem as shown in the diagram below.

Problem

A block of mass M is pulled by a chain of uniform  mass tied to the mass. We need to know the tension in the chain at a particular place. The problem is as shown in the diagram below.

Solution

We know that the chain is uniform and hence its mass is equally distributed. As the point where we need to measure the tension is at one forth of the total length its mass also will be one forth of the total mass of the chain. Thus we can divide the system into two masses. The first one is the mass of the block and the remaining mass of the chain and the second part is one forth of the chain. We can write equations of motion and solve the problem as shown in the diagram below.

Problem

In the given problem two masses are connected with the help of the string as shown in the diagram below. The first mass is on the smooth horizontal surface. The second mass is connected to the firs with the help of a pulley and stand as shown. We need to find the relation between the acceleration of the bodies.

Solution

We can assume that the tension in the horizontal wire is one value and the same will be continued in the connected string. The tension in the bottom wire connected the other bod is the sum of the same two tensions as shown in the diagram below. So we can find the relation as shown here.

Problem

Two blocks of masses are at rest connected with a string over the pulley as shown in the diagram below. A force is applied on the pulley and we need to know the acceleration of the blocks. The problem is as shown in the diagram below.

Solution

The force applied on  the pulley is divided across the two strings equally and hence we know the tension in each wire. We know that the weight of each block acts in down ward direction and the tension in the upward direction. By applying laws of motion and resultant force equation, we can solve the problem as shown in the diagram below.

Problem

A particle is at rest at a given position and force is applied along the X direction. We need to measure the velocity of the particle when it is at a particular distance from the origin. The problem is as shown below.

Solution

We know that the work done is stored in the form of change in kinetic energy. As the body is initially at rest, its initial kinetic energy is zero and hence change in kinetic energy is nothing but final kinetic energy. We can write the work done in terms of integration and the problem is solved as shown in the diagram below.

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