Box with mass attached to spring and board

AI Thread Summary
The discussion revolves around a physics problem involving a wood block attached to a spring, where the block compresses 4.0 cm and stretches 0.9 cm beyond equilibrium. Participants clarify the interpretation of distances, noting that it doesn't matter which direction is considered positive or negative, as long as a consistent convention is applied. The primary goal is to determine the coefficient of friction using the conservation of mechanical energy principles. One participant acknowledges their approach is correct but seeks clarity on the problem's requirements. Overall, the conversation emphasizes understanding the problem's context and the correct application of physics equations.
12boone
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Homework Statement



A 0.580Kg wood block is firmly attached to a very light horizontal spring. It is noted that the block-spring system (k=160N/m), when compressed 4.0cm and released, stretches out 0.9 cm beyond the equilibrium position before stopping and turning back.

Homework Equations



Conservation of Mechanical Energy

KEf+PEf=KEi+PEi

and

1/2kx^2

The Attempt at a Solution



Ok, What I tried to do is solve for the work of friction using

(coefficient of friction)(Normal Force)(d)=1/2k(xf-xi)^2. However, I do not understand what the problem is asking as far as distances. I converted the distance to m but I still do not know what they mean by compressed for 4 cm. Does that mean they pushed it 4 cm forward. Let it go and it went past its resting point .9 cm. If so is .9 negative? or is 4 cm negative?
 
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12boone said:
However, I do not understand what the problem is asking as far as distances. I converted the distance to m but I still do not know what they mean by compressed for 4 cm. Does that mean they pushed it 4 cm forward. Let it go and it went past its resting point .9 cm. If so is .9 negative? or is 4 cm negative?
That would be correct.

However, you have failed to state what the question is asking you to find.
 
what I am looking for is the coefficient of friction.
 
12boone said:
what I am looking for is the coefficient of friction.
Ahh right. Looking back at the question, is doesn't matter which (extension/compression) you choose as positive and which you choose as negative provided that one is positive and one is negative.

Your approach is correct by the way.
 
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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