1. The problem statement, all variables and given/known data Mechanical crane raises 225kg at a rate of 0.031m/s^2. from a rest to a speed of 0.5m/s over a distance of 4m. Frictional resistance is 112N. m1=225kg a1=0.031m/s^2 u1=0m/s v1=0.5m/s s=4m Fr=112N A. Work input from the motor B. Tension in the lifting cable C. Max power developed by the motor. D. Using D'Alembert's principle, solve a) b) c) 2. Relevant equations Wd = ΔPE + ΔKE + Wf (Wf = Work done to overcome friction) Fnet = ma Wd = Fs Weight =m(a+g) PE = mgh KE = mv^2/2 D'Alembert's principle; ΣF = 0 Mechanical Power P = Energy used/Time taken P = FV v=u+at t=(v-u)/a Wd = Work done 3. The attempt at a solution PEi = mgh = 225x9.81x4 = 8829J (incorrect) PEi = mgh = 225x9.81x0 = 0J PEf = 0 (as the energy is transformed to KE) (incorrect) PEf = mgh = 225x9.81x4 = 8829J KEi = 0 (starts from a rest) KEf = mv^2/2 = 225(0.5x0.5)/2 = 28.13J Wd to overcome friction during motion: Wd = Fs = 112x4 = 448J Wd (motor) = (PEf - PEi) + (KEf - KEi) + Wf = (8829 - 0)+(28.13-0)+448 = 8352.87 Therefore the engine Wd would be 8352.87J B) Tension in the rope: Tension = weight + Fnet = (ma)+(mg) In this case the acceleration of the mass is opposite the acceleration of gravity therefore the formula would be. This is assuming Tension during the acceleration of the mass upwards. Tension =m(a+g) =(225x0.031)+(225x9.81) =2214.23N force of tension on the rope c.) P=Fv =(rope tension + Ff)0.031 = (2214.23+112)0.031 = 72.11W D'Alemberts principle states that the total forces must add upto 0. Im not sure how I could show this. To me the power output seems to low and I feel like im missing something on energy when calculating the work done, any help would be mucho appreciated sorry about the math grammar.