8.7 Free body diagram (application)  (Page 2/3)

The forces on the block – 1 are :

• $W_1=m_{1}g=$ its weight, acting downward
• $N_1=$ normal force on block – 1 due to the surface of table, acting upward
• $T_1=$ tension in the string, towards right

The forces on the block – 2 are :

• $W_2=m_{2}g=$ its weight, acting downward
• $N_2=$ normal force on block – 2 due to the surface of table, acting upward
• $T_1=$ tension in the string, towards left
• $T_2=$ tension in the string, towards right

We note here that “mass-less” string passes over a “mass-less” pulley and no friction is involved. As such, the tensions in the string on either side of the pulley are equal.

The forces on the block – 3 are :

• $W_3=m_{3}g=$ its weight, acting downward
• $T_2=$ tension in the string, acting upward

Since strings are taught, it is evident that the acceleration of the blocks and string are same. Also, we note that motion of the blocks on the table is in horizontal direction only. There is no motion in vertical direction. The forces in the vertical direction, therefore, constitute a balanced force system. Thus, for the analysis of motion, the consideration of forces in vertical directions for blocks of masses “ $m_1$ ” and “ $m_2$ ” is redundant and can be simply ignored. Now, taking these two considerations in account, the FBD of the blocks are as shown here :

We should note that the FBD of the blocks show acceleration. Idea here is that we should supplement FBD with as much information as is available. However, we have deliberately not shown the coordinate system which may be selected, keeping in mind the inputs available.