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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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A ball is launched with an initial velocity of 3m/s, at an angle of 40 degrees above the horizontal, and from a height of 0.5m.

Brut [27]

Answer:

The ball travels <u>1.31 m horizontally</u> before hitting the ground.

Explanation:

Given:

Initial velocity of the ball is, $u=3\ m/s$

Angle of projection is, $\theta=40\ degree$

Initial height of the ball is, $y_0=0.5\ m$

Final height of the ball is, $y=0\ m$

Now, horizontal and vertical components of initial velocity are given as:

$u_x=u\cos\theta\\\\u_y=u\sin\theta$

Plug in the given values and find $u_x\ and\ u_y$ . This gives,

$u_x=3\ m/s\times \cos(40)\\\\u_x=2.3\ m/s\\\\u_y=3\ m/s\times \sin(40)\\\\u_y=1.9\ m/s$

Now, there is acceleration due to gravity acting in the vertical direction. The direction is downward. So, $g=-9.8\ m/s^2$ .

Now, using equation of motion in the vertical direction, we have:

$y-y_0=u_yt+\frac{1}{2}a_y t^2$

Plug in the given values and solve for time 't'. This gives,

$0-0.5=1.9t-0.5\times 9.8\times t^2\\\\-0.5=1.9t-4.9t^2\\\\4.9t^2-1.9t-0.5=0$

On solving the above quadratic equation, we get:

$t=0.57\ s\ or\ t=-0.18\ s$

Ignoring the negative result as time can't be negative. So, time taken by the ball to reach the ground is 0.57 s.

Now, as the ball moves, there is no force acting on it in the horizontal direction. So, the acceleration in the horizontal direction is 0.

Now, we know that, when acceleration is zero, the body moves with a constant speed.

Hence, distance traveled in the horizontal direction is given as:

Horizontal distance = Horizontal component of initial velocity × Time

$R=u_x\times t$

Plug in the given values and solve for 'R'. This gives,

$R=2.3\times 0.57\\\\R=1.31\ m$

So, the ball travels 1.31 m horizontally before hitting the ground.

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3 years ago

What do you mean by acceleration due to gravity?

likoan [24]

It is the acceleration of an object in free fall

Explanation:

When an object is in free fall, it is subjected only to one force: the force of gravity, which pulls the object downward, with a magnitude (near the Earth's surface) which is given by

$F=mg$

where

m is the mass of the object

$g=9.8 m/s^2$ is the acceleration due to gravity

We can apply Newton's second law to the object in free fall:

$F=ma$

where

F is the net force on the object

a is the acceleration of the object

m is the mass

However, since there is only the force of gravity acting on the object, the net force is equal to the force of gravity: so we can equate the two equations, obtaining that

$mg = ma\\\rightarrow a = g$

Which means that the acceleration of an object in free fall (acted upon the force of gravity only) is equal to the acceleration due to gravity, $g=9.8 m/s^2$ .

Learn more about gravity:

brainly.com/question/1724648

brainly.com/question/12785992

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4 0

3 years ago

Juan amd kym have four samples of matter. They are observing and describing the properties of these samples. Which property will

TiliK225 [7]

Answer: The property that will best provide evidence that the samples are solid includes:

--> if the substance has a definite shape,

-->if the substance has a definite volume

--> if it's tightly packed.

Explanation:

According to the kinetic theory of matter, every substance consist of very large number of very small particles called molecules. These molecules, which are made up of atoms that are the smallest particles of a substance that can exist in a free state.

Matter can exist in the following states:

--> Solid state

--> liquid state or

--> Gaseous state.

The general property of a substance that is in gaseous state includes:

--> Definite shape: A substance can be grouped as a solid if it's shape is fixed that is, it doesn't depend on the shape of other materials.

--> Definite volume: A substance can be grouped as a solid if it occupies its own shape. This is due to the force of cohesion among its molecules.

--> Tightly packed: A substance can be grouped as solid if the molecular movements of the particles are negligible.

From the samples under observation by Juan and kym, if the sample that possesses the above described qualities, it is a solid rather than liquid or gas.

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3 years ago

Match these items.

Nitella [24]

Explanation :

(1) Involuntary muscles are the muscles that are not controlled by our will.

(2) Tendons are the connective tissues that join the muscle to bones. Tendons are tissues that have fibers.

(3) Cardiac muscle is also involuntary muscles. For example heart muscle. It shows contraction and relaxation throughout life.

(4) Voluntary muscle is the muscles that are not controlled by our will.

(5) Biceps are the arm muscles.

Hence, this the required explanation as per options.

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3 years ago

A 8.34 × 103-kg lunar landing craft is about to touch down on the surface of the moon, where the acceleration due to gravity is

Mnenie [13.5K]

Answer:

21870.3156 N

Explanation:

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 1.6 m/s²

Equation of motion

$v^2-u^2=2as\\\Rightarrow a=\frac{v^2-u^2}{2s}\\\Rightarrow a=\frac{0^2-18.2^2}{2\times 162}\\\Rightarrow a=-1.02234\ m/s^2$

The acceleration of the craft should be 1.02234 m/s²

$F=ma\\\Rightarrow F=8.34\times 10^3\times 1.02234\\\Rightarrow F=8526.3156\ N$

Weight of the craft

$W=mg\\\Rightarrow W=8.34\times 10^3\times 1.6\\\Rightarrow W=13344\ N$

Thrust

$F_t=F+W\\\Rightarrow F_t=8526.3156+13344\\\Rightarrow F_t=21870.3156\ N$

The thrust needed to reduce the velocity to zero at the instant when the craft touches the lunar surface is 21870.3156 N

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3 years ago