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3 years ago

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A Ferris wheel with 60 spokes has a diameter of 100 m. It makes one rotation every 60 seconds. Find the speed of the passengers

when the Ferris wheel is rotating at this rate.

1 answer:

Doss [256]3 years ago

7 0

Answer:

<em>The speed of the passengers is 5.24 m/s</em>

Explanation:

<u>Uniform Circular Motion </u>

It occurs when an object in a circular path travels equal angles in equal times.

The angular speed can be calculated in two different ways:

$\displaystyle \omega=\frac{v}{r}$

Where:

v = tangential speed

r = radius of the circle described by the rotating object

Also:

$\omega=2\pi f$

Where:

f = frequency

Since the frequency is calculated when the number of revolutions n and the time t are known:

$\displaystyle f=\frac{n}{t}$

The Ferris wheel has a diameter of 100 m and makes n=1 rotation in t=60 seconds, thus the frequency is:

$\displaystyle f=\frac{1}{60}\ Hz$

The angular speed is:

$\displaystyle \omega=2\pi \frac{1}{60} =\frac{\pi}{30} \ rad/s$

Now we calculate the tangential speed, solving this formula for v:

$\displaystyle \omega=\frac{v}{r}$

$v=\omega . r$

The radius is half the diameter, r=100/2=50 m:

$\displaystyle v=\frac{\pi}{30} . 50$

Calculating:

v = 5.24 m/s

The speed of the passengers is 5.24 m/s

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It is given that,

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So, according to the law of conservation of energy

$\frac{mgL}{2} = \frac{1}{2}kx^{2} + \frac{1 \times mL^{2}}{2 \times 3}(\frac{\nu}{L})^{2}$

$\frac{mgL}{2} = \frac{1}{2}kx^{2} + \frac{1}{6}mv^{2}$

Putting the given values into the above formula as follows.

$\frac{mgL}{2} = \frac{1}{2}kx^{2} + \frac{1}{6}mv^{2}$

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3 years ago

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Answer:

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Given parameters:

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Answer:

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