## Sunday, November 13, 2016

### Laws of Motion Problems with Solutions Eight

The concepts are here to deal with laws of motion. We are solving regarding rocket propulsion and tension in the string. Rocket is a variable mass as its fuel gets ejected per each  second and the mass of the rocket will be keep on decreasing. We do also solve some problems based on the strings and their connected with the bodies.

Problem

It is given in the problem that fuel of 50 kilogram is consumed per second from the tail of a rocket. We need to measure the thrust on the rocket if the velocity of the exhaust gas is given to us. We also need to measure velocity of the rocket when its mass is reduced to one tenth of its mass. The problem is as  shown in the diagram below.

Solution

As mass is variable with time, force is here the product of rate of change of mass with velocity and its value is given to us. The data is substituted as shown in the diagram below.

We know the formula for the final velocity of the rocket and it is simplified as shown in the diagram below.

Problem

This is also a similar problem like the previous one. The speed of the gas is given to us coming from the rocket and we need to measure the upthrust received by the rocket. The problem is as shown below.

Solution

It is solved using the same concept applied in the previous problem and the solution is as shown below.

Problem

The pulleys and the string shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, we need to know the  angular separation and the problem is as shown in the diagram below.

Solution

We know that because of weight tension is generated in each wire and it acts away from the weight as shown in the diagram below. This tension can be resolved into components. By equating the forces acting in the vertical direction during the balanced condition, we can solve the problem as shown in the diagram below.

Problem

It is given in the problem that a man of mass 60 kilogram is standing on a weighing machine kept in a box of known mass 30 kilogram as shown in the diagram below. If the man manages to keep the box stationary, the reading in the weighing machine is ?

Solution

We need to solve the problem by drawing free body diagrams and further writing the equations of motion. The solution is as shown in the diagram below.

Here we are using the concept that normal reaction is the reading of the scale.

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