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Assignment on Importance of the Pendulum in Science

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Added on  2020-05-28

Assignment on Importance of the Pendulum in Science

   Added on 2020-05-28

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Running head: ASSIGNMENT 51Assignment 5NameInstitution
Assignment on Importance of the Pendulum in Science_1
ASSIGNMENT 52Assignment 5Question 1Part a ∮CF⋅ⅆr⃗F=y^i+x^j+xyz^k⃗r=x^i+y^j+z^kd⃗r=dx^i+dy^j+dz^k⃗F.d⃗r=ydx+xdy+xyzdzBut C=x2−y2=1, z=0,dz=0⃗F.d⃗r=ydx+xdy+xyzdz=ydx+xdy(sincez=0)∮CF⋅ⅆr=∮C(ydx+xdy)=∮C0dxdy=0¿0(sincex,ytakesamepointsforthestarting∧endpoints)Part b∫S∇×F⋅nⅆSz=2x2+y2, ∅=x2+y2−zThe vector that is normal to the surface, ∇∅=∂∅∂x^i+∂∅∂y^j+∂∅∂z^k∇∅=2x^i+2y^j−^k
Assignment on Importance of the Pendulum in Science_2
ASSIGNMENT 53~nds=∇∅¿∇∅.^k∨¿dxdy¿¿2x^i+2y^j−^k|−1|dxdy¿2x^i+2y^j−^k1dxdy∇×F=[^i^j^k∂∂x∂∂y∂∂zyxxyz]=^i(xz−0)−^j(yz−0)+^k(1−1)¿xz^i−yz^jOn the surface, x2+y2≤1,z=0∇×F=xz^i−yz^j=0^i−0^j=0∫S∇×F⋅nⅆS=∫S0⋅nds=0Question 2I=∫∫SzezdsThe equation of the unit sphere is x2+y2+z2=1, z2=1−x2−y22zdzdx=−2x⇒dzdx=−xz2zdzdy=−2y⇒dzdy=−yz
Assignment on Importance of the Pendulum in Science_3

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