Q36 of 149 Page 195

The pulleys in figure (10-E6) are identical, each having a radius R and moment of inertia I. Find the acceleration of the block M.


The acceleration of the block M is


Given


The blocks are of “m” and “M” masses, with radius of r pulley and moment of Inertia “I”


Formula Used


The formula used to find the acceleration of the mass pulled/pushed is determined by the second law of Newton when the Force/Tension applied is equivalent to the product of mass and acceleration



where


is the force of the mass in terms of tension, is the acceleration and m is the mass of the block.


Explanation


The tension produced by the larger masses M is given and the smaller mass m is given as , and the tension between the pulley is therefore, the tension on both the masses are:


……1


and


……2


Now the acceleration of the pulley after deriving from angular acceleration is




Putting the value of tensions and inertia into the equation gives us acceleration as



More from this chapter

All 149 →
34

A string is wrapped on a wheel of moment of inertia 0.20 kg-m2 and radius 10 cm and goes through a light pulley to support a block of mass 2.0 kg as shown in figure (10-E5). Find the acceleration of the block.


 35

Suppose the smaller pulley of the previous problem has its radius 5.0 cm and moment of inertia 0.10 kg-m2. Find the tension in the part of the string joining the pulleys.

 37

The descending pulley shown in figure (10-E7) has a radius 20 cm and moment of inertia 0.20 kg-m2. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is 1.0 kg.


 38

The pulley shown in figure (10-E8) has a radius 10 cm and moment of inertia 0.5 kg-m2 about its axis. Assuming the inclined planes to be frictionless, calculate the acceleration of the 4.0 kg block.