Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle formed by the point (0, 0), (1, 1) and (1, 3). Find the work done by the force field F(x,y)=4yi+2xj in moving a particle along a circle x^2+y^2=1 from(0,1)to(1,0).

ddaeeric 2021-01-05 Answered
Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle formed by the point (0, 0), (1, 1) and (1, 3).
Find the work done by the force field F(x,y)=4yi+2xj in moving a particle along a circle x2+y2=1 from(0,1)to(1,0).
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Expert Answer

Adnaan Franks
Answered 2021-01-06 Author has 92 answers
Step 1
According to the given information, it is required to calculate the work done by the force field
F(x,y)=4yi + 2xj
moving along the particle along a circle x2+y2=1
from(0,1)to(1,0)
Step 2
The work done can be calculated as:
work done = CF.dr
Step 3
Solving further to get:
CF.dr
r(t)=(sint)i+(cost)jfor0tπ2
r(t)=(cost)i+(sint)j
CF.dr=0π2((4cost)i+(2sint)j).((cost)i+(sint)j)dt
=0π2(4cos2t2sin2t)dt
=0π2(6cos2t2)dt
=π2
Therefore, the total work done by the force field is π2.

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