Assume that an enough large asteroid (m = 30,000 kg) coming from the deep space (out of our galaxy so assume at infinity) with a velocity 15 km/s travels through our solar system. When it approaches the Earth, the scientists say that it would be attracted by the Earth and then would impact her. So we would like to research the impact of the asteroid if it hits to our planet. (The Earth radius: RE = 6.4x10° m, and the Earth mass: MĘ = 6.0x104 kg.) a) Write expressions for the initial mechanical energy of the asteroid and the final mechanical energy of the asteroid as it reaches the earth's surface. Do not plug in numbers for this first step. b) What would be the kinetic energy of the asteroid as it reaches the earth? c) What would be the speed of the asteroid as it reaches the earth? d) Now, assume that the asteroid makes a totally inelastic collision with the Earth, i.e., the asteroid embeds itself in the earth's surface. Find the final velocity of the earth, assuming it was at rest initially. e) How much energy would be released in this collision? (Note: a ton of TNT is 4.1x10° J)

Assume that an enough large asteroid (m = 30,000 kg) coming from the deep space (out of our galaxy so assume at infinity) with a velocity 15 km/s travels through our solar system. When it approaches the Earth, the scientists say that it would be attracted by the Earth and then would impact her. So we would like to research the impact of the asteroid if it hits to our planet. (The Earth radius: RE = 6.4x10° m, and the Earth mass: MĘ = 6.0x104 kg.) a) Write expressions for the initial mechanical energy of the asteroid and the final mechanical energy of the asteroid as it reaches the earth's surface. Do not plug in numbers for this first step. b) What would be the kinetic energy of the asteroid as it reaches the earth? c) What would be the speed of the asteroid as it reaches the earth? d) Now, assume that the asteroid makes a totally inelastic collision with the Earth, i.e., the asteroid embeds itself in the earth's surface. Find the final velocity of the earth, assuming it was at rest initially. e) How much energy would be released in this collision? (Note: a ton of TNT is 4.1x10° J)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: The asteroid 243 Ida has a mass of about 4.0×10¹⁶ kg and an average radius of about 16 km (it's not…

A: Mass , m = 4.0 x 1016 kgRadius , R = 16 km = 16 x 103 mTo find = a) launch speed of rock .…

Q: Titan is the largest moon of Saturn, and the only moon in the solar system known to have a…

A: Given Radius = 2570 km = 2570 × 103 m Mass of astronaut m = 60 kg Weight = 81 N Gravitation…

Q: (a) Calculate the work (in MJ) necessary to bring a 104 kg object to a height of 991 km above the…

A: Given that: The mass of an object is m=104 kg The earth's mass is M=5.97×1024 kg The height is h=991…

Q: A comet of mass me is in an elliptical orbit around the sun (mass Mo), which is located at one focus…

Q: A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The…

A: Mass of asteroid m = 5×109 Kg Mass of earth M = 5.97×1024 kg Vi = 810m/s Vf = ? H = 4×106 km Radius…

Q: Comet C/2022 E3 (ZTF) was discovered by astronomers using the wide-field survey camera at the Zwicky…

A: Given: At the closest approach to Earth, Distance between the comet and the center of Earth,…

Q: (a) What is the escape speed on a spherical asteroid whose radius is 106 km and whose gravitational…

Q: The planet Saturn has an average radius of 9 Earth radii and a density of 0.7 g/cm3 (yes, less dense…

A: The distance at which a moon can orbit a planet without disintegrating by its tidal forces is called…

Q: Calculate the escape velocity to an orbit of 317 km height from a planet with the radius of 2000 km…

Q: The expression we developed in class for the angular momentum (per unit mass of the orbiting comet…

A: Given: Expression developed in class earlier, Angular momentum is Lm=2πa21-e2P…

Q: A satellite is in a circular orbit 380 km above the Earth's surface. Find the orbital period and the…

A: For the satellite, gravitational force acting on the satellite due to earth acts as centripetal…

Q: Meteorite A has a mass that is twice as great as Meteorite B. It impacts the desert with a speed…

Q: An exoplanet is in an elliptical orbit around a distant star. At its closest approach, the exoplanet…

Q: The orbit of a 1.5 x 1010 kg comet around the Sun is elliptical, with an aphelion distance of 33.0…

A: The problem based on the concept of a two-body central force problem. According to Kepler's first…

Q: A projectile is fired vertically from a planet's surface with an initial speed of 6.5 km/s. Neglect…

Q: ) Calculate Jupiter's mass given the acceleration due to gravity at the north pole is 28.328 m/s2…

A: Acceleration due to gravity=28.328m Radius of Jupiter =66850km =66850000m Value of gravitational…

Q: Calculate the escape velocity to an orbit of 334 km height from a planet with the radius of 2000 km…

Q: Given an elliptical orbit with a perigee of 6500 km and a 60,000 km apogee, find the true anomaly of…

Q: The speed of a meteor approaching the earth is measured as 100 m/s at a distance of 900 km from the…

Q: a) What is the difference between the forces due to Uranus on a 1.0 kg mass located at the near side…

A: A) The force because of Uranus on the 1 kg mass on the Titan’s near side can be given as, Here, G,…

Q: An asteroid closely passes the Earth at a range of 17200 mi and relative speed of 7.8 km/s. The…

A: v=Velocity of asteroid=7.8 km/s=7800 m/sS=Specific gravity of asteroid=3ρw=Density of water=997…

Q: The mass of planet Q is one-tenth of the mass of Earth and the radius of planet Q is one-half of the…

A: Definition of gravitational field : Intensity of gravitational field at a point is defined as…

Q: A satellite of mass 200 kg is launched from a site on the Equator into an orbit at 200 km above…

A: Solution: m = 200 kg h = 200 km

Q: (a) What is the escape speed on a spherical asteroid whose radius is 103 km and whose gravitational…

Q: 3. A satellite is being injected into Earth orbit at radial distance ro = 7500 km, 8.784 km/s.…

A: Given: Earth orbit's radial distance from earth is 7500 km Velocity is 8.784 Km/sec Radius of…

Q: A spacecraft departing from a 200 km LEO has a total AV of 10 km/s. Determine the following: a) The…

Q: 5. An asteroid of mass 1.1 x 10 kg must be diverted 7.5 hours before striking the earth. How can…

Q: Let’s imagine that you have an idea for an experiment to fly on NASA’s “Vomit Comet.” (What’s…

A: The droplet is to move in a circular orbit of radius 14 cm or 0.14 mAs it moves in this circular…

Q: Determine the minimum velocity(m/s) necessary to orbit freely about a planet or moon at an altitude…

A: The minimum velocity required to orbit freely is,

Q: (a) What is the escape speed on a spherical asteroid whose radius is 502 km and whose gravitational…

A: radius , R = 502 km = 502 x 103 m gravitational acceleration , ag = 0.87 m/s2 radial speed , v =…

Q: Calculate the surface escape velocities for Mars. rM = 3.3× 106 m, MM = 6 × 1022 kg).

A: Given, radius of mars, rm = 3.3×106 m mass of the mars, M = 6×1022 kg

Concept explainers

Gravitational force

In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.

Acceleration Due to Gravity

In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.

Question

Assume that an enough large asteroid (m = 30,000 kg) coming from the deep space (out of our
galaxy so assume at infinity) with a velocity 15 km/s travels through our solar system. When it
approaches the Earth, the scientists say that it would be attracted by the Earth and then would
impact her. So we would like to research the impact of the asteroid if it hits to our planet. (The Earth
radius: RE = 6.4x10° m, and the Earth mass: MĘ = 6.0x104 kg.)
a) Write expressions for the initial mechanical energy of the asteroid and the final mechanical
energy of the asteroid as it reaches the earth's surface. Do not plug in numbers for this first
step.
b) What would be the kinetic energy of the asteroid as it reaches the earth?
c) What would be the speed of the asteroid as it reaches the earth?
d) Now, assume that the asteroid makes a totally inelastic collision with the Earth, i.e., the
asteroid embeds itself in the earth's surface. Find the final velocity of the earth, assuming it
was at rest initially.
e) How much energy would be released in this collision? (Note: a ton of TNT is 4.1x10° J)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Given and Required

VIEW

Initial and final mechanical energy of the asteroid and the final kinetic energy

VIEW

Final velocity of the asteroid at the surface of Earth

VIEW

Velocity of Earth after collision

VIEW

Energy released in the collision

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Find the escape velocity ve for an object of mass m that is initially at a distance R from the center of a planet of mass M. Assume that R≥Rplanet, the radius of the planet, and ignore air resistance. Express the escape velocity in terms of R, M, m, and G, the universal gravitational constant.
Can you please help me with this question please? Thank you so much!
The Apollo 11 spacecraft was placed in an elliptical orbit around the moon. The point in a lunar orbit nearest the surface of the moon is called the perilune, and the point fattest from the surface is called the apolune. The Apollo's orbit had a perilune altitude of 110 km and an apolune altitude of 314 km above the moons surface. Find the equation of this ellipse and radius of the moon is 1728 km and the centre of the moon is at one focus
An asteroid closely passes the Earth at a range of 17200mi and a relative speed of 7.8km/s.The diameter is estimated at 30mwith a specific gravity of 3. If this asteroid had impacted Earth, how much energy would have been released? Express this quantity in units of mega-tons (M ton) where a megaton is the energy released by one million metric tons of TNT explosive. A metric ton is 1000kgand the explosive energy density of TNT is 4184J/g.Hint: If the asteroid hits the Earth, its relative velocity becomes zero. Ignore any change in asteroid velocity due to gravitational acceleration or air resistance.
If you took the Earth and reduced its radius to one fourth its current size, what would the escape velocity from the Earth be?
10
Designing an interplanetary mission from Earth to Jupiter. Given the position and velocityvectors for the Earth parking orbit, r = 8228 I +389 J +6888 K (km)v = -0.7 I +6.6 J -0.6 K (km/s) 1.) Assuming that the satellite will enter the Hohmann transfer elliptical orbit from perigee of its current Earth parking orbit, determine the total velocity increment, Δvtotal required for a Hohmann transfer from the Earthparking orbit to 200km altitude Jupiter parking orbit. 2.) Calculate the semi-major axis, period in earth years, and eccentricity of the Hohmann transfer ellipse.
On February 15, 2013, Asteroid 2012 DA14 passed within 17,200 miles [mi] of the surface of the Earth at a relative speed of 7.8 kilometers per second [km/s]. This is considerably closer than the orbit of geosynchronous satellites (26,200 miles). This is the closest recorded approach of an object this large. The asteroid 2012 DA14 was estimated to have a diameter of 30 meters [m] and a specific gravity of 3. If 2012 DA14 had hit the Earth, what is the total amount of energy that would have been released (i.e., what was the kinetic energy of the asteroid)? Express your answer in megatons [Mton]. One megaton is the energy released by one million metric tons of TNT explosive. A metric ton equals 1,000 kilograms [kg], and the explosive energy of TNT is 4,184 joules per gram [J/g].
The escape velocity from the surface of planet A is 5700 m/s. Planet B has the same density but the radius is 1/3 that of planet What is the escape velocity from the surface of planet B in m/s?
In the past, asteroids striking the earth have produced disastrous results. If we discovered an asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. Intense surface heating from the laser could cause surface material to be ejected into space at high speed. How would this deflect the asteroid?
How much energy is required to lift a 10 kg rock from the surface of the Earth and place it in a circular orbit just 10 km above sea level? Assume Earth's radius is about 6371 km.
Let’s imagine that you have an idea for an experiment to fly on NASA’s “Vomit Comet.” (What’s special about this plane? It flies in parabolic paths (aka freefall) which result in near weightlessness. This means that you can ignore the effects of gravity when plan your experiment.) You want to mimic the orbital motion of the planets but by using electrostatic force rather than gravitational. And, instead of a planet, you will be orbiting a droplet of water that is 0.5mm in radius and has an deficit of 1.5 x 106 electrons. The droplet is to orbit around a small (1cm radius) sphere. If you want the droplet to move with an orbital radius of 14cm and period of one minute, what should the charge be on the central sphere? BTW The density of water is 997 kg/m3.