Solving Friction Problem: Acceleration of Lower Block

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The discussion focuses on calculating the acceleration of a lower block subjected to a force and friction. The problem involves two blocks with given masses and a coefficient of kinetic friction. The user sets up free body diagrams and equations for both blocks but struggles to incorporate the friction between them correctly. There is confusion regarding the net forces acting on the blocks and how to express the frictional forces in the equations. The user seeks clarification on the correct formulation to find the acceleration of the lower block.
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Homework Statement


In the diagram shown below, the lower block is acted on by a force, F, which has a magnitude of 64.1 N. The coefficient of kinetic friction between the lower block and the surface is 0.346. The coefficient of kinetic friction between the lower block and the upper block is also 0.346. What is the acceleration of the lower block, if the mass of the lower block is 4.04 kg and the mass of the upper block is 1.86 kg?

http://img266.imageshack.us/img266/7450/knpic0828.png


Homework Equations


ΣF y = ma y

ΣF x = ma x


The Attempt at a Solution



So i set up 2 freebody diagrams, one for each object and I made F net equations. For the top block:

ma = T - μk*mg (1)

The friction comes from the friction between the top block and the bottom block.

and for the bottom it would be:

ma = Fa - Fk - T (2)

In this case the friction comes from the friction between the bottom block and the ground.


So in the second equation I solved for T, subbed it into equation 1 and solved for a, however I am not getting the correct answer. Any ideas?
 
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What happened to the friction between the two blocks in your second equation?
 
How would I write the friction between the two blocks?

ma = Fa - Fk - T - Fk (?)

So would I get,

ma = F - μk* m1g - μk * m2g - T
 
Yes, I think that's correct.

m_2 a= F-(m_1+m_2)g\mu_k-T
 
Hey I still can't get it with that formula.. Can someone help?
 
Did you find the expression for a?
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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