Understanding Normal and Gravity Forces in Stacked Block Structures

[member 428835]

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 $M_t*g$where 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!

 

[Doc Al]

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 $M_t*g$where 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!)

 

[member 428835]

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!

 

[Doc Al]

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 M_t*g and the gravitational force on the bottom block is M_b*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.)

 

[member 428835]

hey thanks doc! this makes a ton of sense. i appreciate your time here.