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Unformatted text preview: we have: F N mg + dm/dt v rel y = 0 In order to find F N we need to have an expression for dm/dt. Lets first find the relation between dm and dl , where dm is the mass of a short rope segment of length dl that falls on the scale during time dt . Since the rope is uniform, the relation between dm and dl is dm/dl = M / L and multiplying both side for dt dm/dt = M/ L dl/dt = -M/L v rel y Note that d/dt is the impact speed of the segment, so v rel y =-dl/dt (v rel y is negative because up is the positive y direction and the rope is falling). Substituting in the equation for the force we have: F N = mg + M/L v 2 rel y To find v 2 rel y you need to note that, until it touches the scale, each point along the rope falls with constant acceleration g, therefore using the usual equation for a motion with constant acceleration we have: v 2 rel y = v 2 rel 0 +2a y y = 0 + 2(-g) (-L/2) = gL and substituting in F N = Mg/2 + MgL/L = 3/2 Mg where m=M/2...
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