## Wednesday, November 9, 2016

### Laws of Motion Problems with Solutions Three

We are solving series of problems on Newton's laws of motion. Here in this post, we are going to deal with problems based on acceleration  and it is rate of change of velocity. We are going to deal with force which is the physical quantity that changes are try to change the state of the body. We are also going to solve a problem based on connected bodies. We need to study the contact force or tension in the string in this case.

Problem

It is given in this problem that a man is sliding down on a rope and the breaking strength of the rope is given to us. We need to know the minimum acceleration with which he need to  slide down so that the rope is not going to break ?

Solution

We know that force due to gravity acts in the down ward direction. The fire man is also going to slide in the down ward direction only. The weight of the man generates of a tension in the string and it is the reason for breaking strength.

We can write a equation for the resultant force as the difference between the forces acting in the same direction and subtracted with the force acting in the opposite direction of the motion. We can write and solve the problem as shown in the diagram below.

Problem

It is given in the problem that a pendulum bob is hanging from the roof of an elevator with the help of light string. When the elevator moves up with uniform acceleration, the tension in the string is given and when the elevator moves down with same acceleration, the tension in the wire is given. If the elevator were stationary, we need to know the tension in the string ?

Solution

When the lift is moving in the upward direction, we know that tension as well as apparent weight increases and hence in the place of effective acceleration as the sum of both acceleration. We can apply the reverse when the lift is going down with acceleration. By adding that equations, we can solve the problem as shown below.

Problem

It is given in the problem that three bodies are on a horizontal friction less table and they are connected as shown in the diagram. They are connected with strings and the system is pulled towards right by applying a known force. Mass of the bodies is given to us and we need to know the tension in the string.

Solution

We have discussed in detail about drawing free body diagrams and concepts of connected bodies  in the chapter in detail. Free body diagram is the representation of all the forces acting on the body that are causing motion to it. We can apply that rules and write equations of motion for each body. It is representation of resultant force acting on the body.

Taking this into consideration, we can solve the problem as shown in the diagram below.

Problem

A body of mass 10 kilogram is moving eastward with a uniform speed and a force of 20 newton is applied to the towards the north. We need to know the magnitude of the displacement after two seconds. The problem is as shown in the diagram below.

Solution

As the body is moving along east with constant velocity along east, we can find its displacement along east after two seconds as the product of uniform velocity and time.

A force is applied on the body along north. Any way the body has no initial velocity along the north and we can measure the acceleration of the body along the north. Thus we can find its displacement along that direction using the second equation of the motion. As this two displacements are perpendicular to each other, the effective can be written in the form of vector and we can find the magnitude of the vector as shown below.

Problem

It is given in the problem that a balloon of known mass is coming down with a known acceleration. If certain mass is detached from it, it starts moving up and what is its acceleration in that case, we need to find out.

Solution

By writing equation of motion and resultant force in both the cases, the problem can be solved quite simply as shown in the diagram below.

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