In order to raise a mass of , a man of mass fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration of relative to the rope. The tension in the rope is (take )
Step 1: Given Data
Given, the mass of the object
Let be the tension on the rope.
Given, the mass of the man
Given that the acceleration is relative to the rope.
Let the acceleration of the rope be and the acceleration of the man be .
Step 2: Equations of Motion
The mass undergoes a downward acceleration.
Similarly, it also undergoes an upward acceleration due to the pulling of the rope.
Hence, the net acceleration can be given as,
Hence, the equation of motion of the man can be written as
Hence, the equation of motion of the object can be written as
Step 3: Solve the Equations
Upon subtracting equation from equation we get,
Step 4: Calculate the Tension
Upon substituting the values of and equation we get,
Hence, the tension of the rope is .