A runner of 60kg accelerates at 2.0 m/s at the start of race calculate the force provided from her legs

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

In a fireworks display, a rocket is launched from the ground with a speed of 18.0 m/s and a direction of 51.0° above the horizon

Masja [62]

Answer:38.66 m

Explanation:

Given

launch angle $\theta =51^{\circ}$

launch velocity $u=18 m/s$

center of mass continue to travel its original Path so it center of mass will be at a distance of

$R=\frac{u^2\sin 2\theta }{g}$

$R=\frac{18^2\sin 102}{9.8}$

$R=32.33 m$

Center of mass will be at $x=32.33 m$

(b)if one of the piece will be at x=26 m then other will be at

$x_{com}=\frac{m_1x_1+m_2x_2}{m_1+m_2}$

$x_{com}=\frac{\frac{m}{2}\cdot 26+\frac{m}{2}\cdot x_0}{\frac{m}{2}+\frac{m}{2}}$

$32.33=\frac{26+x_0}{2}$

$x_0=38.66 m$

8 0

2 years ago

Janetta ran a campaign for student body president, and she really wanted to win. She gave election buttons to everyone and told

SVEN [57.7K]

Answer:

No, because she is hoping that people will vote for her.

Explanation:

Altruism is when you do something for others and have very little expectation of getting something in return. In this case, Janetta expected something in return from her friends. We may not also be sure of the sincerity of Janetta appreciating friendship. From the above definition of altruism, we conclude that Janetta's actions are not altruistic because she hoped that people will vote for her.

3 0

3 years ago

As Douglas considers his wife’s condition, he realizes that the change having the most impact is “the one that began to steal he

Tanya [424]

I believe that the loss of Phyllis' recollections is thought to be the most heartbreaking side effect of her ailment in light of the fact that once a man's memory scatters then piece of the individual begins to vanish with them. A memory holds a considerable measure of essential data, for example, people's identity, where They have lived, and their connections that they have had with individuals.

8 0

3 years ago

1. The number of protons in an atom, unique to each element, is known as the ___________.

Gnoma [55]

Answer:

atomic number

Explanation:

the number of protons in an atom is called its "atomic number"

4 0

2 years ago