How Do You Calculate Forces in a Two-Mass System on an Accelerating Scale-Pan?

[bubakazouba]

Homework Statement

a light scale pan is attatched to a vertical inextensible sring. The scale-pan carries two masses A and B. The mass of A is 400g and the mass of B is 600g. A rests on top of B, as shown in the diagram.
The scale-pan is raised verticaly, using the string with acceleration 0.5 m/s².
a)find the tension in the string.
b)find the force exerted on mass B by mass A
c)find the force exerted on mass B by the scale-pan.

visual representation of the problem http://i1269.photobucket.com/albums/jj597/bubakazouba/test_zps62ac1992.png

Homework Equations

F=ma
g=9.8 m/s²

The Attempt at a Solution

I got a) correct, I just said
Tension-(0.4x9.8 +0.6x9.8)=0.4x0.5+0.6x0.5
Tension-9.8=0.5
tension =9.8+0.5=10.3N
--------------------
b)find the force exerted on mass B by mass A
I think the answer is mg its the weight, because its the only downward force on A so it should be 0.4x9.8=3.92, but its not right.
What am i missing here?
Thanks in advance

 

[tiny-tim]

hi bubakazouba!

b)find the force exerted on mass B by mass A
I think the answer is mg its the weight, because its the only downward force on A so it should be 0.4x9.8=3.92 …

what about the acceleration?

 

[bubakazouba]

what about it?

 

[tiny-tim]

what about it?

you haven't used it

 

[bubakazouba]

why should I use it?

 

[tiny-tim]

why should I use it?

i] it's in the question

ii] F = ma

 

[bubakazouba]

I don't get it why should I use any equation, isn't it obvious the only force that acts on B is the weight, mg

 

[tiny-tim]

that's the LHS of the equation

what about the RHS?​

 

[bubakazouba]

what equation?

 

[bubakazouba]

I feel so stupid right now :'(

 

[Chestermiller]

Draw a free body diagram on A, showing the forces acting on it. Write a force balance on A, recognizing that A is accelerating upward at a rate of 0.5 m/s².

 

[bubakazouba]

ok I got a force 4.12N upwards what does that mean?

 

[Chestermiller]

ok I got a force 4.12N upwards what does that mean?

That's the contact force exerted by mass B on mass A. Now, from Newton's third law of action-reaction, what is the contact force that mass A exerts on mass B?

 

[bubakazouba]

4.12?
but why, why isn't it the weight?

 

[bubakazouba]

4.12?
but why, why isn't it the weight?

 

[Chestermiller]

4.12?
but why, why isn't it the weight?

Because mass A is accelerating upward, and so mass B has to exert enough upward contact force not only to support the weight of mass A (which would be the case if A were in equilibrium), but also to accelerate it. Also, by Newton's third law, the contact force A exerts on B is equal in magnitude and opposite in direction to the contact force B exerts on A.