Three identical bricks are strung together with cords and hung from a scale that reads a total of 32 N. (a) What is the tension in the cord that supports the lowest brick?

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This problem can be solved by drawing the forces acting on each block and writing down an equilibrium condition for each block.

Please see the attached image. Note that, according to the Newton's Third Law, the force from the scale on the block 1 (the top block) will be equal the force from...

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This problem can be solved by drawing the forces acting on each block and writing down an equilibrium condition for each block.

Please see the attached image. Note that, according to the Newton's Third Law, the force from the scale on the block 1 (the top block) will be equal the force from this block on the scale, which is equals the reading of the scale: 32 N.

The equilibrium condition for block 1 is

`T_12 +mg= 32 N` , where `T_12` is the force from the block 2 on block 1. (More accurately, it is the force from the cord connecting the blocks 1 and 2.) The force `mg ` is the weight of the block.

The force `T_12` and the force `T_21 ` are equal, because they both equal the tension in the connecting cord, which has to be the same at every point.

`T_12 = T_21`

The equilibrium condition for block 2 is

`mg+ T_23 = T_21` 

The same weight is used because the blocks are identical.

Similarly, for the block 3,

`mg = T_32` , where `T_32 = T_23` . This force is also equal to the tension in the cord that supports the lowest brick, which what we have to find. Let's denote this force as T: `T = T_32 = T_32 = mg`

Plugging this in in the equilibrium condition for block 2, we get

`mg + mg = T_21` , so `T_21 = 2mg`  and `T_12 = T_21 = 2mg`

Plugging this into the equilibrium condition for block 1 results in

`2mg + mg = 32 N`

3mg = 32 N

So, the weight of each block is `mg = 32/3 =10.67N ` and as shown above, the tension in the cord that supports the lowest block, block 3, is

T = mg = 10.67 N.

 

 

 

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