## Sunday, November 13, 2016

### Laws of Motion Problems with Solutions Seven

Motion is the change in the state of the body with respect to time and space. The bodies always tries to keep their state as it is and this property is called inertia. To change the state of the body, we need to apply a force on the body that is sufficient enough to overcome the existing inertia. We are here solving problems about force and momentum. As per the law of conservation of linear momentum, if no external force is acting on the system, the momentum of the system always remains constant and it is conserved.

Problem

It is given in the problem that a body of mass 10 kilogram is being acted upon a force that varies with time. It is also given that a opposing force is also acting on the same body and it is a constant force of 32 newton. The body is also having some initial velocity and we need to know the final velocity of the body after five seconds. The problem is as shown in the diagram below.

Solution

As force is variable with time, to find the work done, we shall integrate the variable force with time and it can be equated to change in momentum. The given data is substituted in the concept and the problem is solved as shown below.

Problem

It is given in the problem that a block of mass m is starting from the state of rest from the top of a smooth inclined plane of known inclination. It has reached the bottom of inclined plane in one part of the time and to travel further on smooth surface some more time is taken. We need to measure the difference in this momentum in the given time difference and the problem is as shown below.

Solution

We can identify the change in momentum and the momentum of each part with specific direction as it is a vector quantity. As the body after coming to the bottom has constant velocity in the further travel, both the momentum are in the direction as shown with the angular separation. We can find the effective value using the parallelogram law and the solution is as shown in the diagram below. The velocity can be found using equations of motion.

Problem

It is given in the problem that two monkeys are holding each other as shown and one monkey is climbing a rope. The mass of the monkeys are given for us and the maximum tension can be bared by upper monkey is given to us and we need to know what force it shall apply on the ope to carry the second money with it with out breaking its tail.

Solution

Tension in the lower part of the rope as the sum of the weight of that rope and acceleration of the money multiplied by the mass of it. We can find the acceleration of the upper monkey as shown below. Similarly the tension in the upper part also can be found as shown below.

Problem

A shall of mass 100 gram is moving with a speed known along straight line inclined at a know angle. It is divided into two parts and we need to measure the velocity and direction of the second part after explosion. The problem is as shown in the diagram below.

Solution

As there is no external force acting on the system, linear momentum is conserved. We can resolve the momentum into components and it can be solved as shown in the diagram below.

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