Is the Force on a Block on an Incline Dependent on Velocity?

AI Thread Summary
The discussion centers on determining the force exerted by an inclined track on a block sliding down a frictionless incline and transitioning to a semi-circular ramp. The key question is whether this force, identified as the normal force, depends on the block's velocity. It is clarified that at the point where the block begins ascending the ramp, the block experiences centripetal acceleration, which can be calculated using the formula mv²/r. The net force at that point is the sum of the normal force and gravitational force, allowing for the calculation of the normal force by subtracting gravity from the net force. Ultimately, the force is indeed influenced by the block's velocity due to the centripetal acceleration involved.
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hi, I'm stuck on my very first physics homework problem for my junior level mechanics course... i am not sure if the force in this problem is dependent on velocity.

a block of mass m slides down a frictionless incline. it is released at height h above the bottom of the loop. when it reaches the bottom, it begins going up a semi-circle of angle 45 degrees and radius R. the point where it begins going up the semi circle is labeled point A. basically, the block has acquired a certain velocity, and then starts going up a ramp. the point where the ramp begins is point A.

the question is, what is the force by the inclined track on the block at point A?

i realize the force by the track on the block is the normal force, however it appears this force would also be a function of the velocity, and not just of the mass of the block, but i am not sure. i am stuck because i am not sure if the force would simply be the normal force, or if it would be a function of the velocity (i know how to find the velocity).

am i totally wrong, and the force is simply the normal force, and not a function of the velocity? if there is acceleration upward at point A, which is what i suspect, then is it dependent on velocity (as i can only imagine it is)?

any help would be greatly appreciated.

this is problem 2-25 in thornton/marion's classical dynamics, part (a)
 
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heh, i swear I've thought about this problem for a couple of hours total (i looked at it first yesterday), and i just had a breakthrough immediately after i posted the question.

clearly the ramp part of the system can represented as an angular system which has a certain angular velocity at point A. this will allow me to find the acceleration at that point, and thus the force! correct?
 
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I don't think you have to go so far as to change to an angular representation of the objects position, if that's what you're saying. You know the block is undergoing centripetal acceleration, so you can use mv^2/r to find the net force on it. This is equal to the normal force plus gravity, so subtract gravity and you have your answer.
 
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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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