Solve Strange Problem: Beginner's Guide

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To solve the problem, start with the equation F = m*a and consider the forces acting on the object, including weight and normal force. Analyze a simpler scenario involving a ball on an inclined block, where the block accelerates in the positive x-direction while the ball remains stationary vertically. Establish force equations in both x and y directions using Newton's second law to determine the acceleration. The discussion emphasizes understanding the balance of forces and setting up equations correctly. Continued attempts and practice are encouraged for better comprehension and preparation.
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Can someone tell me how to do this problem? I Don't even know where to begin.
 

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Begin with F=m*a.
You should use that, and the fact that the resultant of that force and of m*g is along the normal to the surface in the equilibrium position.
 
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Consider a simpler problem first: The ball on block with a constant incline. Assume the block is accelerated towards the +x direction and that the ball is not moving vertically on the block.

The ball will experience two forces: Its weight and a normal force coming from the incline W,\ N . Assume the incline is at an angle \theta w.r.t. the horizontal. What can you say that the acceleration will be given by in such a situation?
 
Can you set up the force equations in the x- and y-directions using Newton's second law?

That is: "The sum of the force components on an object in the x (or y) direction is equal to its mass times its acceleration in the x (or y) direction"
 
Thanks for the help guys. I still couldn't get it, though. I'll give it another crack soon for test preparation.
 
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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