Normal force between stacked boxes

[jackattack825]

Homework Statement

The UPS person is delivering two rectangular boxes to the 4th floor of a building. The boxes are stacked vertically in the elevator. The one on the bottom has a mass of 5.00 kg and the one on the top has a mass of 2.00 kg. The elevator, the UPS person, and both boxes are accelerating upward at 2.50 m/s^2. What is the magnitude of the normal force between the two boxes?

Relevant Equations

Force(net) = mass * acceleration

Σ F= -F(gravity from earth) + F(normal from earth) -F(normal from top box) +F(normal from bottom box) = (2+5) * 2.5
The forces from gravity and it's normal force cancel out, leaving us with the normal forces from the boxes.

F(net of normal from boxes) = (2+5) * 2.5
= 17.5N

 

[PhanthomJay]

No. You seem to be looking at the system of both boxes, where their combined weight acts down, and the normal force of the elevator on the bottom box acts up. That’s it, the other normal forces are internal and do not enter in your equation. Try looking at a free body diagram of the top box. The problem asks for the normal force between the 2 boxes.

 

[jackattack825]

thanks for the speedy response

the free body diagram for the top box would just be gravity pulling down and a normal force from the other box pushing up, correct?

EDIT: based on that logic, I got F(normal)= m(g+a) or 2(-9.8+2.5)= 14.6N

 

[PhanthomJay]

thanks for the speedy response

the free body diagram for the top box would just be gravity pulling down and a normal force from the other box pushing up, correct?

Yes

EDIT: based on that logic, I got F(normal)= m(g+a) or 2(-9.8+2.5)= 14.6N

No. The acceleration is given as a, not a + g. Try again, using the net force (the algebraic sum of
both forces ) acting on the box, on the left side of your equation.

 

[jackattack825]

No. The acceleration is given as a, not a + g. Try again, using the net force (the algebraic sum of
both forces ) acting on the box, on the left side of your equation.

So you are saying:

F(normal) - F(gravity) = ma , F(normal) - 9.8= 2 * 2.5 , F(normal)= 5+9.8= 14.8N

 

[PhanthomJay]

The acceleration of gravity is 9.8 m/s^2, but you are looking for the force of gravity, not the acceleration of gravity.

 

[jackattack825]

ah i got it now

F(normal) -F(gravity) =ma
F(normal) - 9.8*2 = 2*2.5
F(normal) = 5+19.6 = 24.6N

 

[PhanthomJay]

Yup!