How Does a Ferris Wheel Affect the Forces on a Rider?

[chooch]

A Ferris wheel that rotates three times each minute and has a diameter of 16.0 m

What force [magnitude and direction (measured inward from the vertical)] does the seat exert on a 43.0 kg rider when the rider is halfway between top and bottom, going up?

Ok, the magnitude is easy...

Fnet = m(centripetal acceleration^2 + acceleration due to gravity^2)^1/2 = 422.77 N

What I can't figure out to save my life is the direction "measured inward from the vertical"..

My thinking is to basically make a triangle (similarly to the method used to find Fnet) with 33.95 N being the opposite side (pushing in), and the adjacent side being 421.4 N (pushing up). This gives 0.08 degrees in from vertical, which is incorrect.

What am I doing wrong here?

Thanks!

 

[learningphysics]

opposite is 33.95. adjacent is 421.4. What is arctan(33.95/421.4) ?

 

[andrevdh]

The rider is experiencing two forces, the seat (diagonally up and inwards) and his weight (down) these two together produce the (horizontally inwards) centripetal force.

Fnet (the diagonal I get a bit different from you 427 N). The angle that is required is therefore between the weight and Fnet vector.

Also I do not get a vector of 33.95 N in my calculations.

 

[learningphysics]

The rider is experiencing two forces, the seat (diagonally up and inwards) and his weight (down) these two together produce the (horizontally inwards) centripetal force.

Fnet (the diagonal I get a bit different from you 427 N). The angle that is required is therefore between the weight and Fnet vector.

Also I do not get a vector of 33.95 N in my calculations.

I'm getting 33.95N. v = 3.14(16)*3/60 = 2.513m/s. mv^2/r = 43*(2.513)^2/8 = 33.95

 

[chooch]

OK... This is the second time this semester I've made myself look like a fool because I was in radian mode...

Sorry... the answer is indeed arctan(33.95/421.4).

 

[learningphysics]

OK... This is the second time this semester I've made myself look like a fool because I was in radian mode...

Sorry... the answer is indeed arctan(33.95/421.4).

Don't feel bad. I've made that same mistake a couple of times right here on the forum!

 

[andrevdh]

Ok, I took the diameter for the radius in my calcs.