How to demostrate k in Hook' s law?

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To demonstrate the spring constant k in Hook's Law, a vertical spring setup can be used with a mass hung at the end. By measuring the stretch of the spring and the force applied (the weight of the mass), multiple trials with different masses can be conducted. This data allows for the plotting of a graph of force (F) versus displacement (x). The slope of this graph remains constant and is equal to the spring constant k. This experimental approach effectively illustrates the relationship defined by Hook's Law.
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How to demostrate k in Hook' s law?
 
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Experimentally, you could probably use a spring setup where a spring is suspended vertically, and a mass is hung at the end. You measure the length of stretch of the spring, as well as the force applied to it (which is the weight of the mass). Doing multiple trials with different masses will give you enough data to plot a graph of F vs. x. You will notice that the slope of this line is constant, and it is equal to k.
 
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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