We are solving a series of problems on laws of motion and its applications. In this post we are going to deal with rocket motion linked problems. We need to use the concept of force. Force is defined as the rate of change of momentum. If the mass of the body is constant, it will become the product of mass and rate of change of velocity which is also called as acceleration. If velocity of the body is constant and mass is variable, force will be the product of velocity and rate of change of mass.
Problem
It is given in the problem that a rocket of 400 kg mass is set for vertical firing and the speed with which the gas ejects from its back is given in the problem. We need to know how much of the gas has to be burned by the rocket so that it can move upward with an acceleration equal to acceleration due to gravity. The problem is as shown in the diagram below.
Solution
We can apply second law of newton law of motion. Here in this problem, mass of the rocket is constant rather it is variable. As certain mass of the rocket is ejected per each second, mass of the rocket will be keep on changing with time and we need to apply the second concept of the formula.
While writing the effective acceleration of the system, we need to add acceleration of the rocket moving up and acceleration due to gravity as they are in opposite direction and and we need to take relative acceleration.
By substituting the data, we can solve the problem as shown below.
Problem
This problem is also regarding rocket propulsion. Rate of the ejection is given to us and the velocity of the gas ejection is also given to us and we need to measure the acceleration of the rocket with which it moves up. The problem is as shown in the diagram below.
Solution
We can apply the same concept of the previous problem and solve it as shown below. We are just using the Newton's second law of motion.
Problem
A block of mass is placed on a smooth horizontal surface and it is connected to massive string with the mass similar to block.If a force is applied on the string other end, we need to know the tension at the mid point of the rope. The problem is as shown in the diagram below.
Solution
We need to know the tension in the wire at its middle. So we need to consider a point of the rope which is at its middle having a mass half of the total mass of the rope. At that point, we need to consider the forces acting and we shall write the equations of motion as shown in the diagram below.
Problem
In this problem, a body of known mass is suspended by two strings making known angles with the horizontal. We need to find the tensions in the string. The problem is as shown in the diagram below.
Solution
We need to apply Lami's theorrem to solve the problem. We know that according to that theorem, the force and its ratio with sin angle is constant. The solution is as shown below here.
Problem
It is given in the problem that the vertical distance between the two bodies is given and we need to know when it becomes zero. The problem is shown below.
Solution
Using the equations of motion, we can find the acceleration of the system. It is part of discussion we have made about connected bodies earlier. If one moves up ward and the other down ward by the same distance, then they look like having zero separation. Thus each one shall have a displacement equal to half of given separation. The problem is as shown in the diagram below.
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