Fitzpatrick Water-ski question (1 Viewer)

[serge]

hey
has anyone properly finished the fitzpatrick circular motion question
in 35c (q14 i think) about a boat, and a water-skiier?
i dont need a full explanation, just which vectors you resolved... and if resistance in this question is mkv^2 or kv^2?

 

[serge]

for people that don't have fitzpatrick i'll add the whole question...

A water skier of mass 100kg is towed by a boat, the length of the tow rope is 30m. the boat's speed is constant at 8ms and the skier's is 10ms. the total mass of the boat and its occupant is 300kg.
assuming the tow rope is horizontal and total air and water resistance is proportional to the square of the speed (with the same constant of proportion for both boat and skier) find the tension in the rope, and the magnitude and direction of the force driving the boat.

thanks in advance

 

[Trev]

We did this in class.... *thinks*

 

[Trev]

Hope you can understand this...
EDIT: Supposed to say Fc [F_c] in second part, not Fx.

 

[serge]

thanks for that... but part of the working says cosa=5/3
isnt it meant to be cosa=3/5? therefore 120N of tension.

 

[serge]

it seems that all the worked solutions that ive found are geared to find the solution at the back of the book, not to make mathematical sense

 

[Trev]

I... don't... know...

 

[Roobs]

Ive just hit this question and am insanely confused......still....for my benifit, could someoen post a complete proof?
would be
greatly appreciated

 

[Riviet]

Basically what Trev has in his attachment is correct [except that it's cos(a)=3/5 not 5/3]. "a" is the angle at the point (in the triangle) where the skiier is. The diagram at the bottom is a little confusing. Also note that the diagrams are from a bird's eye view.

 

[Roobs]

hmm..yeah i figured out the first part of the question ok--but the diagram at the bottom just lost me for the second part--basically i cant figure out the in which direction the force driving the boat should act--at a tangent to the circle? at an angle directed into the circle? or out of the circle?

if somone could help me with that i think im set-- just a matter of resolving into tangential and radial components and equating
Tangential to resistance + tension in rope
Radial to mv^2/r

?????