# Ferris Wheel Rotation physics

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!

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

andrevdh
Homework Helper
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
Homework Helper
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

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