This problem is driving me crazy

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AI Thread Summary
The discussion revolves around a spring scale experiment involving three weights, with specific focus on determining the equilibrium point when no weight is attached and calculating the weight of package C. The user is analyzing the differences in displacement and force between weights A and B to apply Hooke's Law, which states that force is proportional to the spring constant and displacement. They initially calculated a difference of 20 mm and 88 N between the two weights, leading to a potential spring constant of 4.4. The user expresses confusion but is beginning to grasp the concepts involved. The conversation highlights the application of physics principles to solve the problem effectively.
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Homework Statement


A spring with a pointer attached is hanging next to a scale marked in millimeters. Three different weights (weights A, B and C) are hung from the spring, in turn, as shown below. Weight A weighs 111 N and B weighs 199 N.

there are three pictures of spring scales with weights attached: the first spring with weight A attached is at 40mm the second (with weight B) is at 60mm and the third (with weight C) is at 30mm

(1) Which mark on the scale will the pointer indicate when no package is hung from the spring?
(2) What is the weight of package C?

The Attempt at a Solution


right now I'm just thinking about part 1 so i found the difference in mm and N between A and B so i found 20mm and 88N and I'm pretty sure this is relevant, but I'm really confused and don't know where to go from here!
 
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The first part is basically just asking you to figure out the equilibrium point of the spring. When the mass is hanging from the spring, what keeps the mass from just falling to the floor? Just what does hooke's law say?
 
so F=kx
88=k20
so the answer would be 4.4?
 
Hooke's law says that the force is proportional to the spring constant and the displacement.

F = -k \Delta x
 
ok i think I'm starting to get it now...thanks
 
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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