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2 years ago

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A space station consists of three modules, connected to form an equilateral triangle of side length 82.0 m. Suppose 100 people,

with an average mass of 75.0 kg each, live in each capsule and the mass of the modules is negligible compared to the mass of the people. At the current rotational rate the effective acceleration of gravity is g/2. (a) What angular momentum of the system

1 answer:

CaHeK987 [17]2 years ago

8 0

Answer:

Angular momentum of the system is 16221465.4617 kgm²/s

Explanation:

Given that;

length of the side of the triangle L = 82 M

m = 75.0 kg × 100 = 7500 kg

distance of each vertex from center R = L/√3 = 82/√3 = 47.34 m

effective acceleration a = 9.8 / 2 = 4.9 m/s²

we know that; effective acceleration is being provided by centripetal acceleration.

so

a = R × w²

rate of rotation w = √( a / R) = √( 4.9 / 47.34) = 0.3217 rad/seconds

Moment of Inertia I = 3mR²

we substitute

I = 3 × 7500 × (47.34)²

Also, Angular momentum L is expressed as;

L = I × w

so

L = 3 × 7500 × (47.34)² × 0.3217

L = 16221465.4617 kgm²/s

Therefore, Angular momentum of the system is 16221465.4617 kgm²/s

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Q1 is located at the origin, Q2 is located at x = 2.50 cm and Q3 is located at x = 3.50 cm. Q1 has a charge of +4.92μC and Q3 ha

Inessa05 [86]

Answer:

$+1.11\mu C$

Explanation:

A charge located at a point will experience a zero electrostatic force if the resultant electric field on it due to any other charge(s) is zero.

$Q_1$ is located at the origin. The net force on it will only be zero if the resultant electric field intensity due to $Q_2$ and $Q_3$ at the origin is equal to zero. Therefore we can perform this solution without necessarily needing the value of $Q_1$ .

Let the electric field intensity due to $Q_2$ be + $E_2$ and that due to $Q_3$ be - $E_3$ since the charge is negative. Hence at the origin;

$+E_2-E_3=0..................(1)$

From equation (1) above, we obtain the following;

$E_2=E_3.................(2)$

From Coulomb's law the following relationship holds;

$+E_2=\frac{kQ_2}{r_2^2}\\$

$-E_3=\frac{kQ_3}{r_3^2}$

where $r_2$ is the distance of $Q_2$ from the origin, $r_3$ is the distance of $Q_3$ from the origin and k is the electrostatic constant.

It therefore means that from equation (2) we can write the following;

$\frac{kQ_2}{r_2^2}=\frac{kQ_3}{r_3^2}.................(3)$

k can cancel out from both side of equation (3), so that we finally obtain the following;

$\frac{Q_2}{r_2^2}=\frac{Q_3}{r_3^2}................(4)$

Given;

$Q_2=?\\r_2=2.5cm=0.025m\\Q_3=-2.18\mu C=-2.18* 10^{-6}C\\r_3=3.5cm=0.035m$

Substituting these values into equation (4); we obtain the following;

$\frac{Q_2}{0.025^2}=\frac{2.18*10^{-6}}{0.035^2}\\\\hence;\\\\Q_2=\frac{0.025^2*2.18*10^{-6}}{0.035^2}\\$

$Q_2=\frac{0.00136*10^{-6}}{0.00123}=1.11*10^{-6}C\\\\Q_3=+1.11\mu C$

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3 years ago

an object of mass m is rotating about a fixed axis with angular momentum l. its moment of inertia about this axis is i. what is

Tems11 [23]

The Kinetic energy would be 1/2IL².

<h3>What is Rotational Kinetic energy ?</h3>

Rotational energy also known as angular kinetic energy is defined as: The kinetic energy due to the rotation of an object and is part of its total kinetic energy. Rotational kinetic energy is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity.

As we know linear Kinetic energy = 1/2mv²

where m= mass and v= velocity.

Similarly rotational kinetic energy is given by = 1/2IL²

where I- moment of inertia and L=angular momentum.

To know more about the Kinetic energy , visit:

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1 year ago

What do each of the variables mean ? <br> F=__________ m=_________<br>a=___________<br>

wariber [46]

Answer:

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Explanation:

This is Newton's Second Law!

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3 years ago

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bezimeni [28]

Answer:

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For both the second example, it also has the $v_o$ velocity, but the kinetic energy is higher among the three because its potential and kinetic energy are higher.
While over the last case the kinetic speed is greater and lower than in the first case, the total energy is also higher than the first lower than that of the second.
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2 years ago

Which of these objects has kinetic energy?

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3 years ago

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