Log in
Physics
1
answer
4
watching
487
views

Earth is rotating about the Sun in our solar system. The distance between the Earth and Sun
is 1.5 × 1011m. Consider the impact of an asteroid of mass 8.9 ×1015 kg and a speed of 90,000
km/h with respect to the Earth’s surface. The asteroid strikes the Earth at the equator as shown
in Figure. Consider the mass and radius of the Earth are ME = 5.97 × 1024 kg and RE = 6.38
×106 m, respectively. Assume that the axial and orbital axis of rotations are parallel to each
other.

(a) Calculate the axial and total angular momentum of the Earth. (4 marks)
(b) What is the change in the angular velocity of the Earth due to the collision? (6 marks)
(c) What is the maximum possible change in the length of a day due to the collision?
(3 marks)
(d) How much energy is needed to stop the Earth’s rotation about its axis after the collision?
(4 marks)
(e) What would be the moment of inertia of the Earth if the axis of rotation is parallelly
shifted so that it touches the equator?

Watch
1
answer
4
watching
487
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Avatar image
Read by 3 people

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share

Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Consider a spherical asteroid with a radius of 27 km and a mass of8.25 multiplied by 1015 kg. Assume the asteroid is roughlyspherical.
Suppose the asteroid spins about an axis through its center, likethe Earth, with a rotational period T. What is the smallest value Tcan have before loose rocks on the asteroid's equator begin to flyoff the surface?

calculate the angular momentum of the earth in its orbit around the sun?

 

 

m   5.97 10 kg 6 E R   6.38 10 m Orbital radius 11 r   1.50 10 m Period of rotation Prot = 24 h 86,400 s  Period of revolution Prev = 7 1 y 3.156 10 s   Identify: L I z z   Set Up: For a particle of mass m moving in a circular path at a distance r from the axis, 2 I mr  and v r   . For a uniform sphere of mass M and radius R and an axis through its center, 2 2 5 I MR  . The earth has mass 24 E m   5.97 10 kg , radius 6 E R   6.38 10 m and orbit radius 11 r   1.50 10 m . The earth completes one rotation on its axis in 24 h 86,400 s  and one orbit in 7 1 y 3.156 10 s   . Execute: (a) 2 24 11 2 40 2 7 2 rad (5.97 10 kg)(1.50 10 m) 2.67 10 kg m /s 3.156 10 s L I mr z z z                   . The radius of the earth is much less than its orbit radius, so it is very reasonable to model it as a particle for this calculation. (b)   2 2 2 24 6 2 33 2 5 5 2 rad (5.97 10 kg)(6.38 10 m) 7.07 10 kg m /s 86,400 s L I MR z z                  Evaluate: The angular momentum associated with each of these motions is very large. Note that the orbital angular momentum is over 7 orders of magnitude greater than its rotational angular momentum. In fact, most of the total angular momentum of the solar system comes from the sum of the orbital angular momenta of its planets.

In Example 34.6 (page 1111), we imagined equipping 1950DA, an asteroid on a collision course with the Earth, with a solar sail in hopes of ejecting it from the solar system. We found that the enormous size required for the solar sail makes the plan impossible at this time. Of course, there is no need to eject such an object from the solar system: we only need to change the orbit. A much more pressing problem is Apophis, a 300-m asteroid that may be on a collision course with the Earth and is due to come by on April 13, 2029. It is unlikely to hit the Earth on that pass, but it will return again in 2036. If Apophis passes through a 600-m keyhole on its 2029 pass, it is expected to hit the Earth in 2036. causing great damage. There are plans to deflect Apophis when it comes by in 2029. For example, we could hit it with a 10- to 150-kg impactor accelerated by a solar sail. The impactor is launched from the Earth to start orbiting the Sun in the same direction as the Earth and Apophis. The idea is to use a solar sail to accelerate the impactor so that it reverses direction and collides head-on with Apophis at 80–90 km/s and thereby keeps Apophis out of the keyhole. Consider the momentum in the impactor’s orbit (Fig. P34.75) when the solar sail makes an angle of θ = 60° with the tangent to its orbit. Current solar sails may be about 40 m on a side, but the hope is to construct some that are about 160 m on a side. Estimate the impactor’s tangential acceleration when it is about 1 AU from the Sun. Keep in mind that the sail is neither a perfect absorber nor a perfect reflector, and a heavier impactor would presumably be equipped with a larger sail. Don’t be surprised by what may seem like a very small acceleration.

Weekly leaderboard

Home
Homework Help 3,900,000
Physics 110,000
Start filling in the gaps now
Log in