IIT JEE-AIEEE 2012, Entrance Notifications, Study Tips, Engineering Preparation, Practice Test Papers, Experts Advice

ramyani chakrabarty

In solving this type of problem, there is a four step method.

Step no1 Identify the system ( body on which the equn F=ma is to be applied)

Step no2 List all the forces acting on the system.

Step no3 Draw a free body diagram ( a diagram in which we consider the body under consideration as a point and show all forces by lines in proper direction)

Step no4 Finally appply the equn F=ma

Now in the given problem let us first take m₂as the system ( Step no1)
The forces acting on this system are: (step 2)

                1. Weight m₂g in the vertically downward direction.
                2.Tension T of the string in the vertically upward direction.

So the net downward force is m₂g--T. This force accelerates the body in the downward direction with accln a ( say ).

As I cant draw i skip step3.

now step 4.

the equn is Force = mass* accln

                     m₂g -- T = m₂a ..........................(1)

Apply the same process by taking m₁ as a system.
List all forces.These are:
1. wt. m₁g vertically downward.
2. Tensin T up the inclined plane along the string.                               3. Frictional force down the inclined plane (f)

Net upward force along the plane T - m₁g sin alpha - f .

    Here we have resolved m₁g perpendicularly to inclined plane as m₁g cos alpha ( downward) and along the plane m₁g sin alpha ( opposite to direction of tension T i,e, down the inclined plane).

                                    Draw FBD.

Now this body moves up the inclined plane. Equn is

                        T - m₁g sin alpha - f = m₁ a      ............................(2)

now solve.
g = 10 m/s²
alpha = 30 degree

f on m₁ = 0.1 * m₁ * g cos (alpha)     [ remember friction= mu* normal reaction]


From these two equns find result.

P.S. Read H C Verma vol I page 66 for the algorithm.

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