Understanding Normal and Gravity Forces in Stacked Block Structures

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When stacking two blocks, the top block experiences a normal force equal to its weight (M_t) and a gravitational force of M_t*g. The bottom block, however, has a normal force that must balance both its own weight (M_b*g) and the downward force exerted by the top block, resulting in a normal force of M_t + M_b. The gravitational force acting on each block is independent; the top block's gravity is M_t*g, while the bottom block's gravity is M_b*g. Normal forces are reactions to the weights and interactions of the blocks, not gravitational forces. Understanding these distinctions clarifies the equilibrium of forces in stacked block structures.
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why is it when you stack two blocks on each other that the top box with mass M_t has a normal force of M_t and a gravity force M_t*gwhere as the bottom box has a normal force of M_t+M_b where M_b is the mass of the bottom box yet gravity is M_b*g?

i guess i don't get why gravity is the same for each box the the normal force considers all the weight stacked on top (why doesn't gravity?)

thanks for your help!
 
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joshmccraney said:
why is it when you stack two blocks on each other that the top box with mass M_t has a normal force of M_t and a gravity force M_t*gwhere as the bottom box has a normal force of M_t+M_b where M_b is the mass of the bottom box yet gravity is M_b*g?

i guess i don't get why gravity is the same for each box the the normal force considers all the weight stacked on top (why doesn't gravity?)

thanks for your help!
The normal force is whatever is needed to keep the blocks in equilibrium. The normal force exerted by the bottom block on the top block need only balance the weight of the top block.

But the normal force from the floor on the bottom block must balance both the weight of the bottom block and the downward normal force that the top block exerts on the bottom block. Those two forces add up to equal the weight of both blocks.

(Be careful not to use the same symbol for mass and normal force!)
 
i appreciate your reply! can you explain why the gravity force acting on the bottom block (when considering the free body diagram) is simply M_b*g rather than (M_b+M_t)*g. this concept is killing me.

i appreciate your time!
 
joshmccraney said:
i appreciate your reply! can you explain why the gravity force acting on the bottom block (when considering the free body diagram) is simply M_b*g rather than (M_b+M_t)*g. this concept is killing me.
The gravitational force on anything is simply its weight. The gravitational force on the top block acts on the top block, not on the bottom block. (Of course the downward normal force that the top block exerts on the bottom block happens to equal the weight of the top block.)

So regardless of whatever else is going on between them, the gravitational force on the top block is Mt*g and the gravitational force on the bottom block is Mb*g.

Remember: The gravitational force on a block is a force exerted by the earth on the block. The forces that the blocks exert on each other are normal forces, not gravitational forces. (They may well be equal in magnitude to the weight, but they are not gravitational forces.)
 
hey thanks doc! this makes a ton of sense. i appreciate your time here.
 
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