Which unit would you use to express the height of your desk?

Asteroid Ida was photographed by the Galileo spacecraft in 1993, and the photograph revealed that the asteroid has a small moon,

Nady [450]

Answer:

The orbital speed of Dactyl is $5.55m/s$

Explanation:

The orbital speed can be determined by the combination of the universal law of gravity and Newton's second law:

$F = G\frac{M \cdot m}{r^{2}}$ (1)

Where G is gravitational constant, M is the mass of the asteroid, m is the mass of the moon and r is the distance between them

In the other hand, Newton's second law can be defined as:

$F = ma$ (2)

Where m is the mass and a is the acceleration

Then, equation 2 can be replaced in equation 1

$m\cdot a = G\frac{M \cdot m}{r^{2}}$ (2)

However, a will be the centripetal acceleration since the moon Dactyl describe a circular motion around the asteroid

$a = \frac{v^{2}}{r}$ (3)

$m\frac{v^{2}}{r} = G\frac{M \cdot m}{r^{2}}$ (4)

Therefore, v can be isolated from equation 4:

$m \cdot v^{2} = G \frac{M \cdot m}{r^{2}}r$

$m \cdot v^{2} = G \frac{M \cdot m}{r}$

$v^{2} = G \frac{M \cdot m}{rm}$

$v^{2} = G \frac{M}{r}$

$v = \sqrt{\frac{G M}{r}}$ (5)

Finally, the orbital speed can be found from equation 5:

Notice, that it is necessary to express r in units of meters.

$r = 95km \cdot \frac{1000m}{1km}$ ⇒ $95000m$

$v = \sqrt{\frac{(6.672x10^{-11}N.m^{2}/kg^{2})(4.4x10^{16}kg)}{95000m}}$

$v = 5.55m/s$

Hence, the orbital speed of Dactyl is $5.55m/s$

3 0

2 years ago

5. Forces have

Verdich [7]

5)

In physics, forces are interactions that are able to change the velocity of an object.

Force is a vector quantity, so it has a magnitude and a direction.

The SI units of the force is the Newton (N).

Whenever an unbalanced force is applied to an object, the object experiences an acceleration, according to Newton's second law of motion:

$F=ma$

where

F is the force

m is the mass of the object

a is its acceleration

So, the acceleration of an object is proportional to the force applied:

$a=\frac{F}{m}$

6)

In physics, arrows are used to represent vector quantities. Therefore, they are also used to represent forces.

In particular, when a vector quantity is represented by an arrowr:

- The length of the arrow is proportional to the magnitude of the vector quantity

- The direction of the arrow corresponds to the direction of the vector quantity

Therefore, if a force is represented through an arrow:

- The length of the arrow shows the strength (magnitude) of the force

- The direction of the arrow shows the direction of the force

7)

As we said in part 5), the SI units of the force is the Newton (N).

We can rewrite the Newton in terms of fundamental units only. We can do it starting from the equation:

$F=ma$

where

F is the force

m is the mass

a is the acceleration

- The mass is measured in kilograms (kg)

- The acceleration is measured in meters per second squared ( $m/s^2$ )

Therefore, 1 N corresponds to:

$[N]=[kg][\frac{m}{s^2}]=[kg\cdot m \cdot s^{-2}]$

B)

Gravity is an attractive force that exists between all objects that have mass. See more explanations about gravity in part 4).

3)

Mass is a scalar quantity; it gives us a measure of the "amount of matter" contained in an object.

The SI unit of the mass is the kilogram (kg).

Being a scalar, mass has no direction, but only a magnitude.

Moreover, the mass is an intrinsec property of an object: therefore, it does not depend on the location of the object. So, an object has always the same mass, either it is on Earth or on another planet.

On the other hand, the force of gravity on an object depends on its location, so it changes.

4)

As we said in part 3), gravity is an attractive force that exists between all objects that have mass.

The magnitude of the force of gravity between two objects is given by the Universal Law of gravitation:

$F=\frac{Gm_1 m_2}{r^2}$

where

G is the gravitational constant

m1, m2 are the masses of the two objects

r is the separation between the objects

From the equation above, we observe that:

- all objects are attracted to one another with a gravitational force that is proportional to the mass of the objects and inversely proportional to the square of the distance between them.

And so:

a. When the mass of one or both objects increases, the gravitational force between the objects increases

b. When the distance between two objects increases, the attraction between the objects decreases

7 0

3 years ago

A gas has an initial volume of 212 cm3 at a temperature of 293 K and a pressure of 0.98 atm. What is the final pressure of the g

Serggg [28]

If the ga has 212 cm3 the. Temperature was at a 2

7 0

3 years ago

Read 2 more answers

a plane is flying due east in still air at 395 km/h. suddenly, the plane is hit by wind blowing at 55km/h toward the west. what

Sphinxa [80]

Let's be clear: The plane's "395 km/hr" is speed relative to the
air, and the wind's "55 km/hr" is speed relative to the ground.

Before the wind hits, the plane moves east at 395 km/hr relative
to both the air AND the ground.

After the wind hits, the plane still maintains the same air-speed.
That is, its velocity relative to the air is still 395 km/hr east.
But the wind vector is added to the air-speed vector, and the
plane's velocity <span>relative to the ground drops to 340 km/hr east</span>.

6 0

3 years ago

The Andromeda galaxy is the closest major galaxy to our own. Andromeda shows a distinct blue-shift of light when we analyze it.

saul85 [17]

At the present time, the only way we know of that light can get shifted
toward the blue end of the spectrum is the Doppler effect ... wavelengths
appear shorter than they should be when the source is moving toward us.

IF that's true in the case of the Andromeda galaxy, it means the galaxy is
moving toward us.

We use the same reasoning to conclude that all the galaxies whose light is red-shifted are moving away from us. That includes the vast majority of all galaxies that we can see, and it strongly supports the theory of the big bang
and the expanding universe.

If somebody ever comes along and discovers a DIFFERENT way that light
can get shifted to new, longer or shorter wavelengths, then pretty much all
of modern Cosmology will be out the window. There's a lot riding on the
Doppler effect !

4 0

3 years ago