cutemimi said: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.)
zimbob said: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.
The formula for calculating workdone on a helix is W = ∫ F · T · ds, where W is the workdone, F is the force applied, T is the tangent vector, and ds is the infinitesimal displacement along the helix.
The variable W represents the workdone, which is the amount of energy transferred to an object when a force is applied to it. The variable F represents the force applied to the object. The variable T represents the tangent vector, which is the direction of motion along the helix. The variable ds represents the infinitesimal displacement along the helix.
Calculating workdone on a helix is important because it allows us to understand the amount of energy being transferred to an object as it moves along a helix. This information can be useful in various fields such as engineering, physics, and biomechanics.
Workdone on a helix is different from workdone on a straight path because the direction of motion is constantly changing along a helix, while it remains constant along a straight path. This means that the force and displacement vectors are not always parallel to each other, leading to a different calculation for workdone.
Yes, the same formula for calculating workdone on a helix can be applied to other curved paths, as long as the force and displacement vectors are known at every point along the path. This formula is a generalization of the work-energy theorem and can be applied to any path, curved or straight.