What is the Maximum Acceleration of a Towed Block on an Inclined Plane?

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The discussion focuses on determining the maximum acceleration of two connected blocks on an inclined plane. It establishes that the tension in the towing string cannot exceed mg√3 for block A to maintain contact with the slope. Additionally, it highlights the need to analyze the forces acting on the blocks, including normal and parallel components, to understand the system's behavior. The ratio of tensions in the two strings is shown to be √3:4, regardless of the system's acceleration. Understanding these principles is crucial for solving the problem effectively.
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Homework Statement



Two identical blocks A & B each of mass, m, are connected together by a light string, S1, and are placed on a smooth plane inclined at 30degrees to the hotizontal. A second string, S2, is attached to block A and is used to tow the blocks up the slope with S2 inclined at 30degress to the slope.

a) Show that if block A is to remain in contact with the slope, the tension in S2 cannot exceed mg.sqrt3 and hence find the maximum possible acceleration of the system.

b) Show that the ration between the tensions in S1 and S2 is sqrt3 : 4, independent of the acceleration of the system

Homework Equations


All the equation you may need to use


The Attempt at a Solution


Dont know where to start from. When the questions states if block A needs to remain in contact.. its confusing me.
 
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The thing is that the string is at an angle to the slope and thus tends to lift block A off the slope. You'll have to find the normal force(s) and find the value of the string force that makes the total normal force zero (liftoff).
 
i know the principle, i just can't come to prove it... if anyone can show me the first lines.
 
Can you find the component of mg that is normal - straight into the slope? Then do the same for the string force. If you can't see it, draw a diagram and show the forces separated into normal and parallel to the ramp components.
 
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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