Homework SourseA particle travels along the helix c given by rtcostisintj2t
A particle travels along the helix c given by r(t)=cost(i)+sint(j)+2t(k) and is subject to a force F=xi + zj -xyk. Find the total work done on the particle by the force for 0 < t < 3Pi.
Solution
Work = Integral(F.r) = integral(F.r) from t= 0 to 3Pi = x cos(t) + z sin(t) -xy (2t) dt from t=0 to 3pi = [xsin(t) - zcos(t) - xyt^2] from t=[0] to t=[3pi] =[0 +z -9xy*pi^2] -[0 - z + 0] = [2z -9 xy*pi^2]
