Home Work #1 Due Date: 11 Feb, 2010 (Turn in your assignment at the mail box of S581 outside the ME general office) The solutions must be written on single-side A4 papers only.

HW 1-Problem #1 The beam is subjected to the parabolic loading. Determine an equivalent force and couple system at point A. F=2.667kN M RA =0.667kN.m

HW 1-Problem #2 Two couples act on the frame. If the resultant couple moment is to be zero, determine the distance d between the 500-N couple forces. D=1.663m M1=500*0.9*sin60 M2=-500*(0.9+d)*sin60 M3=-750*(1.8+d)*3/5 M4=750*[(1.8+d)*3/5+1.2*4/5] M1+M2+M3+M4=0 D=1.663m

HW 1-Problem #3 The five ropes in figure can each take 1500N without breaking. How heavy can W be without breaking any? 7F=W 4F=1500N W=7*1500/4=2625N F F 2F 4F

HW 1-Problem #4 The man in figure weighs 800N. He pulls down on the rope, raising the 250-N weight. He finds that the higher it goes, the more he must pull to raise it further. Explain this, and calculate and plot the rope tension T as a function of θ. What is the value of the tension, and the angle θ, when the man can lift it no further? Neglect the sizes and weights of the pulleys.

HW 1-Problem #5 Two small balls A and B have masses m and 2m, respectively. They rest on a smooth circular cylinder with a horizontal axis and with radius R. They are connected by a thread of length 2R. Find the angles θ 1 and θ 2 between the radii and the vertical line OC for equilibrium, as well as the tension in the thread and forces exerted by A and B on the cylinder. Assume that the balls are very small and that the tension is constant. FFFaFb θ1θ1 θ2θ2 Fa*sin θ 1 =F*cos θ 1 Fa*cos θ 1 +F*sin θ 1 =m Fb*sin θ 2 =F*cos θ 2 Fb*cos θ 2 +F*sin θ 2 =2m sin θ 1 = 2sin θ 2 θ 1 =84.73 θ 2 =29.86 F=mgsin θ 1 =0.9958mg N Fa=mg cos θ 1 =0.0919mg N Fb=2mg cos θ 2 =1.7345mg N mg2mg