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Nikitich [7]
3 years ago
15

How many revolutions per minute would a 20 m -diameter ferris wheel need to make for the passengers to feel "weightless" at the

topmost point?
Physics
1 answer:
timurjin [86]3 years ago
6 0
The general equation for the forces acting on the passengers at the topmost point of the ferris wheel is
mg - R = m \omega^2 r
where
mg is the weight of the passengers
R is the normal reaction of the cabin
m \omega^2 r is the centripetal force

In order to feel weightless, the normal reaction felt by the passengers should be zero. Therefore, the equation becomes:
mg=m \omega^2 r
or
g=\omega^2 r
where \omega is the angular frequency of the wheel and r is its radius. Since we know its radius, 
r= \frac{20 m}{2}=10 m
we can calculate the angular frequency:
\omega= \sqrt{ \frac{g}{r} } = \sqrt{ \frac{9.81 m/s^2}{10 m} } =0.99 rad/s
From which we find the frequency at which the ferris wheel should rotate:
f= \frac{\omega}{2 \pi}= \frac{0.99 rad/s}{2 \pi}=0.158 s^{-1}
This is the number of revolutions per second, so the number of revolutions per minute will be
f=0.158 s^{-1} \cdot 60 = 9.48 min^{-1}
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Answer:

Solution ( for fourth attachment ) : 38°C

Tip : Remember the units °C when submitting answer

Explanation:

As you mentioned, we only need the solution for the fourth attachment.

The idea here is that the heat lost by the metal will be equal to the heat gained by the water. We know that the specific heat gained or lost will always be represented by the following formula,

q = m * c

Therefore if we substitute the know values and equate the two equations knowing that " q " is common among them --- ( 1 )

0.33 * 448

Remember that the change in temperature of iron (ΔT) would be represented by final temperature - initial temperature, or final temperature - 693. Similarly the change in temperature of water will be final temperature - 39. Now we can pose the final temperature as a, and solve for a through substitution --- ( 2 )

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From here on take a look at the attachment. It represents how to receive get a through simple algebra. Here a, the final temperature, is about 38°C. In exact terms it will be 38.03617\dots°C.

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