If the distance doubles, what happens to the force?

In a large centrifuge used for training pilots and astronauts, a small chamber is fixed at the end of a rigid arm that rotates i

RSB [31]

a) The length of the arm of the centrifuge is 10.9 m

b) The angular acceleration is $2.7 rad/s^2$

Explanation:

a)

In a uniform circular motion, the centripetal acceleration is given by

$a_c=\omega^2 r$

where:

$\omega$ is the angular speed of the circular motion

r is the radius of the circle

For the centrifuge in this problem, we have:

$\omega=1.7 rad/s$ is the angular speed

The centripetal acceleration is 3.2 times the acceleration due to gravity ( $g=9.8 m/s^2$ ), so:

$a_c=3.2 g = 3.2(9.8)=31.4 m/s^2$

Therefore, we can re-arrange the previous equation to find r, the radius of the circle (which corresponds to the length of the arm of the centrifuge):

$r=\frac{a_c}{\omega^2}=\frac{31.4}{1.7^2}=10.9 m$

b)

In the second part of the exercise, the centrifuge speeds up from an initial angular speed of 0 to a final angular speed of 1.7 rad/s. The total acceleration experienced at the final moment is

$a=4.4 g$

So, 4.4 times the acceleration due to gravity.

The total acceleration is the resultant of the centripetal acceleration ( $a_c$ ) and the tangential acceleration ( $a_t$ ):

$a=\sqrt{a_c^2+a_t^2}$

We know that:

a = 4.4g

$a_c = 3.2 g$

So, we can find the tangential acceleration:

$a_t = \sqrt{a^2-a_c^2}=\sqrt{(4.4g)^2-(3.2g)^2}=29.6 m/s^2$

The angular acceleration is related to the tangential acceleration by

$\alpha = \frac{a_t}{r}$

where r = 10.9 m is the length of the centrifuge. Substituting,

$\alpha = \frac{29.6}{10.9}=2.7 rad/s^2$

Learn more about centripetal and angular acceleration here:

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8 0

3 years ago

How to find moment of inertia of hemisphere

gtnhenbr [62]

<span>It’s 2/5 MR^2 where M is mass and R is the radius of the bas</span>

6 0

3 years ago

When a wave is acted upon by an external damping force what happens to the energy of the wave

Nimfa-mama [501]

Answer:

A-the energy of the wave decreases gradually

Explanation:

when a wave is acted upon by an external damping force the energy of the wave decreases gradually.

The energy degrades into the form of heat which is considered to be of less value and use. The reason is because it disperses and spreads more widely.

So therefore it end up as heat with a little sound but that is close to none because that too disperses into heat i.e. decreased form of energy.

4 0

3 years ago

A person is lying on a diving board 3.50 m above the surface of the water in a swimming pool. She looks at a penny that is on th

sergij07 [2.7K]

Answer:

1.995 m

Explanation:

Distance of penny as seen by the person = 5 m

Height of person from water surface = 3.50 m

Apparent depth of penny = 5 - 3.50 = 1.5 m

refractive index of water, n = 1.33

real depth / apparent depth = n

real depth = 1.33 x 1.5 = 1.995 m

Thus, the actual depth of water at that point is 1.995 m.

4 0

3 years ago

How much does the earth/sky weigh?

Talja [164]

Calculated weight (by experimentally) of Earth is 5.972 × 10²⁴ N

Hope this helps!

6 0

2 years ago