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Anettt [7]
3 years ago
11

Two identical asteroids travel side by side while touching one another. If the asteroids are composed of homogeneous pure iron a

nd are spherical, what diameter in feet must they have for their mutual gravitational attraction to be 1 lb?

Physics
1 answer:
victus00 [196]3 years ago
6 0

Answer:

diameter = 21.81 ft

Explanation:

The gravitational force equation is:

  1. F=\frac{GMm}{R^{2} }

Where:

  • F => Gravitational force or force of attraction between two masses
  • M => Mass of asteroid 1
  • m => Mass of asteroid 2
  • R => Distance between asteroids 1 and 2 (from center of gravity)

We also know that the asteroids are identical so their masses are identical:

  • M=m

Since R is the distance between centers of the two asteroids and their diameters are identical (see attachment), we can conclude that:

  • R=d=2r

We don´t know the mass of the asteroids but we know they are composed of pure iron, so we can relate their masses to their density:

  • m=ρV

This is going to be helpful because the volume of a sphere is:

  • \frac{4}{3}\pi r^{3}

And know we can write our original force of gravity equation in terms of the radius of the asteroids:

  • F=\frac{GMm}{R^{2} } =\frac{Gmm}{(2r)^{2} } =\frac{Gm^{2} }{4r^{2} }
  • F=\frac{G ( \frac{4}{3}\pi r^{3}ρ)^{2} }{4r^{2} }
  • F= \frac{G(16)\pi ^{2} r^{6} ρ^{2}}{(9)(4)r^{2} } =\frac{G(16)\pi ^{2} r^{4}ρ^{2}  }{36}

Now let´s plug in the values we know:

  1. F = 1 lb     mutual gravitational attraction force
  2. G = 6.67(10)^{-11}     gravitational constant
  3. ρ_{iron} =491.5 \frac{lb}{ft^{3} }

  • 1= \frac{6.67(10)^{-11} \pi ^{2} r^{4} (491.5)^{2}}{36}

Solve for r and multiply by 2 because 2r = diameter

  • d=2\sqrt[4]{\frac{1}{7.07(10)^{-5} } }

Result is d = 21.81 Feet

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Answer:

F = 51.3°

Explanation:

The component of weight parallel to the inclined plane must be responsible for the rolling back motion of the car. Hence, the force required to be applied by the child must also be equal to that component of weight:

F = Parallel\ Component\ of\ Weight\ of\ Wagon= WSin\theta\\

where,

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θ = Angle of Inclinition = 20°

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8 0
2 years ago
What is the force felt by the electrons and the nuclei in the rod when the external field described in the problem introduction
fomenos

Complete Question

The complete question is shown on the uploaded image

Answer:

The nuclei experience a force that will move it to the right of the conductor rod while the electrons experience a force that will move it to the left side of the conductor rod.

Explanation:

The force that act on the charges(both the positive and the negative charge ) is Mathematically expressed as

                      F = qE   => E = F/q

where F is the force, q is the charge and E is the electric field

we can see that the force is directly proportional to the electric field,so an increase in the electric field would increase the force.

we can also see that the electric field is given as force per unit charge and generally the direction of this field is taken to be the direction of the force it would exert on a positive test charge

Now from the question we are being told that the external electric field is the direction of the positive x axis

Hence this field would drive the positive charge i.e the nuclei to the right.

In order to further explain let consider this

Generally the electric field is always radially outward  originating from a positive point charge and radially in toward a negative point charge.

what  this means for this question, is that the positive point charge is on the left side of the electric field while the negative point charge is at the right side of the field.

According to Coulomb's law which states that unlike term attract while like terms repel, it means that  the electron would move to the left of the conductor rod   while the nuclei would move to the right side of the conductor rod.

7 0
3 years ago
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skelet666 [1.2K]

Answer:

B is the best answer for the question

6 0
3 years ago
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galben [10]
100 joule of kinetic energy
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Curtis, a student in our class, makes the following statement: The puck reached a slightly higher location on the ramp than I pr
Sindrei [870]

Answer and Explanation: No, the explanation is not plausible. The puck sliding on the ice is an example of the <u>Principle</u> <u>of</u> <u>Conservation</u> <u>of</u> <u>Energy</u>, which can be enunciated as "total energy of a system is constant. It can be changed or transferred but the total is always the same".

When a player hit the pluck, it starts to move, gaining kinetic energy (K). As it goes up a ramp, kinetic energy decreases and potential energy (P) increases until it reaches its maximum. When potential energy is maximum, kinetic energy is zero and vice-versa.

So, at the beginning of the movement the puck only has kinetic energy. At the end, it gains potential energy until its maximum.

The representation is as followed:

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K_{i}+0=0+P_{f}

\frac{1}{2}mv^{2} = mgh

As we noticed, mass of the object can be cancelled from the equation, making height be:

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So, the height the puck reaches depends on velocity and acceleration due to gravity, not mass of the puck.

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3 years ago
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