Calculating Workdone on a Helix using W=Integral F.Tds

[cutemimi]

Homework Statement

Use W=Integral F.Tds
To find workdone when a particle is moved along the helix x=cost, y=sint, z=2t from (1,0,0) to (1,0,4pi) against a force F(x,y,z)=-yi+xj+zk = -sinti+costj+2tk ( substituting above)

Homework Equations

The Attempt at a Solution

Let rt = costi+sintj+2tk
r't= -sinti+costj+2k

Therefore W= Intergral(0tp4pi)[ <-sint,cost,2>.<-sint,cos t,2t>=Intergal[sin^2t+cos^2+2t] = [t+2t^2]from 0 to 4pi

Giving the answer 4pi+32pi^2

 

[dynamicsolo]

Homework Statement

Use W=Integral F.Tds
To find workdone when a particle is moved along the helix x=cost, y=sint, z=2t from (1,0,0) to (1,0,4pi) against a force F(x,y,z)=-yi+xj+zk = -sinti+costj+2tk ( substituting above)

Homework Equations

The Attempt at a Solution

Let rt = costi+sintj+2tk
r't= -sinti+costj+2k

Therefore W= Intergral(0tp4pi)[ <-sint,cost,2>.<-sint,cos t,2t>=Intergal[sin^2t+cos^2+2t] = [t+2t^2]from 0 to 4pi

Giving the answer 4pi+32pi^2

Be careful here: you are integrating the work with respect to the value of the parameter t. What is the value of t at the endpoint of this helical path? (It's not 4·pi.)

 

[cutemimi]

Please assist...I am lost

 

[dynamicsolo]

You can't be all that lost: it looks like your work integral is set up correctly.

The path that the particle travels on is a helix (an ascending circular spiral) starting at (1, 0, 0) and ending at (1, 0, 4·pi). The parametric equation for this path is given as x = cos t, y = sin t, z = 2t . You said you're starting the path integral at t = 0, which corresponds to x = cos 0 = 1 , y = sin 0 = 0 , z = 2·0 = 0 , which checks against the starting coordinates. So what value must t have for the ending coordinates? That is the value you would end your integration of the dot product (1 + 4t) at.

 

[zimbob]

I get the point, and I am now using 2pi as the ending coordinate. My next dump question is having (-1,0,4pi) not (1,0,4pi) when i apply 2pi to the parametric equations.

 

[dynamicsolo]

I get the point, and I am now using 2pi as the ending coordinate. My next dump question is having (-1,0,4pi) not (1,0,4pi) when i apply 2pi to the parametric equations.

cos(2·pi) = ?