# Normal force: two boxes with different mass?

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1. Apr 28, 2015

### spenny23

I took a practice Ap Physics test today and did well, but there was a basic problem that hung me up: there are two boxes on the ground on top of each other. the top box's mass is 2m, and the bottom's is 1m. question: just looking at the bottoms box's normal force, does it equal the 2m box on top? i've learned newton's laws but im really rusty and i understand that if the boxes were switched around, the bottom box (now 2m) would have a normal force of 1mG. , enough to support the top box. but, given the original problem's circumstance, i dont believe that a lighter box on the bottom can apply a normal force to support the top box, without the ground's support: the 1m box on bottom does not have a normal force equal to the top box, 2m. this seems to conflict newton's laws, so i need help realizing if im on the right track or not with this problem.

2. Apr 28, 2015

### PhanthomJay

Well you are a bit off track; Newtons laws and free body diagrams tell no lies when properly applied. So, with the 1m mass on bottom and the 2m mass on top, the normal force of the lower 1m mass on the upper 2m mass is????

3. Apr 28, 2015

### spenny23

the same. for some reason the rest of the test was pretty easy and this problem had other factors (constant velocity elevator, so no worries) that didnt affect the problem so i got all nervous and thought it was a exceptional case.

4. Apr 28, 2015

### spenny23

could you still explain exactly why the small mass on bottom still has 2mG of force to the top? my physics teacher is pretty bad and i've never dealt with normal force problems that involved more than one object (i.e rollercoaster on track. box on slope, etc)

5. Apr 28, 2015

### PhanthomJay

The masses are at rest so Newtons first law applies. Draw a free body diagram of the top mass alone, assuming you are familiar with free body diagrams, which is a necessity. When you do this, you look at all the forces acting on the top mass . The weight of the top mass acts down, and the normal force of the bottom mass on the top mass acts up. So newtons 1st law tells you that if 2mg weight acts down, then the normal force on the top block from the bottom block is how much? Don't say the same, give me a number

6. Apr 28, 2015

### spenny23

2

7. Apr 29, 2015

### PhanthomJay

Yes, 2mg. And when the blocks are reversed, the normal force between the two becomes 1mg.

You are wondering how the 1 m mass when on the bottom can support the 2m mass without issue, and with a force of 2mg. Well, maybe it can't if it is not made of suitable material strong enough to withstand the force without crushing, and even with the heavier mass on the bottom, maybe it can't support the lighter mass either if say the heavy mass was a box with a top surface made of thin paper. This is a strength issue and a separate topic, so assume in these problems that the objects are rather rigid regardless of their mass.