Calculating Total Force on a 1/2 Wavelength Section of a Wave-Rope System

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To calculate the total force on a 1/2 wavelength section of a wave-rope system, first identify the wave equation y = 0.04 cos(3.1 t - 3.5 x) and its parameters. The wave's wavelength can be determined from the wave number, and the tension in the rope must be calculated using the mass and length provided. Using the small-angle approximation simplifies the calculations for forces acting on the rope section. The total force exerted by the rest of the rope can then be derived from these values, ensuring that the weight of the rope is neglected. Completing these calculations will yield the required total force for the homework assignment.
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I could not figure out this question for hw, and it's due in like 5 hours, please someone help me...

At time t = 0, consider a 1/2 wavelength long section of the rope which is carrying the wave y = 0.04 cos(3.1 t - 3.5 x) between two points which have zero displacement (y = 0). Find the total force exerted by the rest of the rope on this section. Neglect any effects due to the weight of the rope. Use the small-angle approximation where q, sin(q), and tan(q) are all approximately equal to each other. Length of the rope is 5m and has mass of 1.5kg.
 
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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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