Energy loss in a pulley, but cleverer

AI Thread Summary
The discussion revolves around calculating energy loss in a pulley system involving a block and friction. The block's mass, radius from the pulley center, moment of inertia, and its downward travel distance and speed are provided. The equation used to find the energy dissipated (Q) includes gravitational potential energy and kinetic energy components. The initial calculation yielded an energy loss of 8.15 J, but there is confusion about whether this value should be negative. Further clarification on the calculation method is requested to resolve the discrepancies in the results.
helloxkitty
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Homework Statement



A block of mass 7.00×10-1kg is suspended by a string which is wrapped so that it is at a radius of 5.80×10-2m from the center of a pulley. The moment of inertia of the pulley is 4.00×10-3kg*m2. There is friction as the pulley turns. The block starts from rest, and its speed after it has traveled downwards a distance of D=0.830m is 1.611m/s. Calculate the amount of energy dissipated up to that point.

given m, r, I, v, D, find Q (energy lost)

Homework Equations



mgh=U(x)
1/2Iw^2
I/2mv^2


The Attempt at a Solution



-mgh=1/2Iw^2+1/2mv^2+Q
solve for Q, get 8.15 J lost. I'm not really sure why I'm unable to get the right answer...unless 8.15 is supposed to be negative. Any thoughts? Thanks so much =)!
 
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Hmm, your method is correct. I got -3.25 as the work done by friction. Show a bit more in depth how exactly you made your calculation.
 
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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