Question

It is from the field of vector calculus, thank you. I have no clue too.

This mask shaped object is cut from a metal sheet weighing lg/cm by a blowtorch which first moves along the closed path parametrized by R (t) until the outer parts of the metal sheet are removed, and then moves along two closed path sections both parametrized by R (t) to cut out the eye-holes of the mask. Ri(t) = 10 cos(t) cos* (t) - sin(t) in(e) cm, Ry(t) = (6sin(t) + sign(sin(t)) 3sin(t)cos(t) + 4 ст Ri(t). R2(t) -10 -10 a) Determine the weight of the work-piece after the R -cut b) Determine the weight of the finished mask after the R -cut Function sign : sign(x) = 1 if x > 0, sign(x) = -1 if x < 0, sign(x) = 0 if x = 0

Answer 1

weight of workpiece after R, cut W = Areax 1 = w gm. 2T1 A = .lt Sathy. dx = { sy. de y=106054-lo sint x = locost dt = -losint 211 2 2 A = S 60 w542-10 sint) Giosint) dt Ifwosit sint +sin't helt "costsinta tl sint dit هدا) - 27 ar 100 - o cost=u 2 xd 20 २ ༢n - lool' ut de + icos - cosat dt) 100141 singel cool(3-5)+=0)) 1 = - cm2 100 T = m. weight 100T. gm (b) Area of ha unt Ri-R R2 =25 (3 sint cost+4) (6 cost) df П

R₂ = 36 sint wst dt+ 48 ( costat 48 host at 0 - cost=u sintaht=-du 1 = 36 = 365 u²(-du) + 48 sintl us 12.11-1-1)) +48.0 -1 24 weight After R₂ cut T-

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