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The original problem is

Figure P6.61 shows a Ferris wheel( I have attached the image) that rotates four times

each minute. It carries each car around a circle of diameter

18.0 m. (a) What is the centripetal acceleration of a

rider? What force does the seat exert on a 40.0-kg rider

(b) at the lowest point of the ride and (c) at the highest

point of the ride? (d) What force (magnitude and direction)

does the seat exert on a rider when the rider is

halfway between top and bottom?

I have already done a), b) and c) with no problem. I also have a solution manual to check and I know that I am correct.

For d) This is my reasoning

[tex]\begin{array}{l}

\sum {{F_r} = m{a_r} = (\ddot r} - r{\left( {\dot \theta } \right)^2}) = \frac{{ - m{v^2}}}{r} = - mg\sin (\theta ) + n\\

n = mg\sin (\theta ) - \frac{{m{v^2}}}{r}\\

\theta = 0,n = \frac{{ - m{v^2}}}{r}

\end{array}[/tex]

however, this is not what the solution manual says. This is what the solution manual says:

[tex]n = m\sqrt {{g^2} + {a_r}^2} [/tex]

I am not dealing with the numbers yet. I want to know why I am wrong and the solution manual is correct. Thankyou.

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# Homework Help: Normal force in Ferris wheel

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