How Do You Analyze Forces in a Non-Slipping Book Stack Scenario?

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In the scenario of analyzing forces in a non-slipping book stack, the top book (ma) is supported by the bottom book (mb) while both are accelerated to the right. The key forces at play include the applied force at a 64° angle, the normal force, friction, and gravitational force. Friction acts to prevent slipping and opposes the horizontal forces acting on the top book. The normal force is influenced by the vertical component of the applied force and the weight of the top book. Understanding these forces is essential for accurately drawing free body diagrams for each book.
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A hand supports two books, ma and mb, with ma on top. The hand accelerates the books p and to the right, with a pushing force directed 64° above horizontal. Assuming the upper book does not slip, draw a free body diagram for each book.

My attempt:
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Which book is on top? and it would help if you defined all of your variables that you have shown.
 
ma is on top
R is the reaction force
n is the normal force
μn is friction
mg is gravity
|Fa| is the applied force
 
What force is friction opposing in order to keep it from slipping?

What is your normal force (or contact force)? Is it the same in this situation as it would be if the books were stationary?
 
Jesse H. said:
What force is friction opposing in order to keep it from slipping?

What is your normal force (or contact force)? Is it the same in this situation as it would be if the books were stationary?
I don't know that's the part I need help with
 
In this problem friction acts only in the x direction. What other forces do you have acting in x? What do you know about those forces if the book doesn't slip?

It might help to say that the reaction force is the force that the bottom book is pushing up on the top book. So the reaction force is actually the y component of your applied force!
 
Last edited:
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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