Q1Using the above equation and what you know about kinetic energy and energyconservation, show that the expression for the escape velocity Ye from a planet of2GMradius R is v, =V R(Hint: To just escape the planet, the object's speed must beO infinitely far from the planet.) and find the escape velocity of an object beinglaunched from Earth. Earth has a radius of 6,360km and a mass of 6.0-10* kg.Q 2Within a certain distance of a black hole, not even light can escape. This distance iscalled the "event horizon." (This was discussed in the online question box earlier thismonth.) The speed of light is 3.0-10° .Even though our equation from part 1 does not hold exactly when considering lightbeams, we can still use it to get a good estimate of the size of a black hole.Estimate the radius of a black hole with the same mass as our sun (2.0 ·10º kg). (Forcomparison, our sun has a radius of about 7.0 ·10°m .) When you throw a ball into the air, it usually falls back down. If you throw it a littleharder, it will take it longer to fall back down. You can throw it so hard that it neverfalls back down to Earth. This launch speed is called the escape velocity.When you are far from Earth, the potential energy of an object with mass m can nolonger be written as PE = mgh. Instead, we must use the equationМ-тPE = -G ..1"M is the mass of the planet you launch from.m is the mass of the object being launched.r is the distance from the center of the planet to the object being launched.G is a universal constant called the gravitational constant (6.67-10-" ).kg-sNotice that the potential energy is 0 when you are infinitely far away from theplanet, and negative as you get closer.

Consider any object of mass m, initially on the surface of the earth. Since this object is on earth,…

Q1 Using the above equation and what you know about kinetic energY and energy conservation, show that the expression for the escape velocity ve from a planet of 2GM radius R is v, = (Hint: To just escape the planet, the object's speed must be R ... O infinitely far from the planet.) and find the escape velocity of an object being launched from Earth. Earth has a radius of 6,360km and a mass of 6.0·10* kg.

Q1 Using the above equation and what you know about kinetic energY and energy conservation, show that the expression for the escape velocity ve from a planet of 2GM radius R is v, = (Hint: To just escape the planet, the object's speed must be R ... O infinitely far from the planet.) and find the escape velocity of an object being launched from Earth. Earth has a radius of 6,360km and a mass of 6.0·10* kg.

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)...

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Question

Q1
Using the above equation and what you know about kinetic energy and energy
conservation, show that the expression for the escape velocity Ye from a planet of
2GM
radius R is v, =
V R
(Hint: To just escape the planet, the object's speed must be
O infinitely far from the planet.) and find the escape velocity of an object being
launched from Earth. Earth has a radius of 6,360km and a mass of 6.0-10* kg.
Q 2
Within a certain distance of a black hole, not even light can escape. This distance is
called the "event horizon." (This was discussed in the online question box earlier this
month.) The speed of light is 3.0-10° .
Even though our equation from part 1 does not hold exactly when considering light
beams, we can still use it to get a good estimate of the size of a black hole.
Estimate the radius of a black hole with the same mass as our sun (2.0 ·10º kg). (For
comparison, our sun has a radius of about 7.0 ·10°m .)

When you throw a ball into the air, it usually falls back down. If you throw it a little
harder, it will take it longer to fall back down. You can throw it so hard that it never
falls back down to Earth. This launch speed is called the escape velocity.
When you are far from Earth, the potential energy of an object with mass m can no
longer be written as PE = mgh. Instead, we must use the equation
М-т
PE = -G ..
1"
M is the mass of the planet you launch from.
m is the mass of the object being launched.
r is the distance from the center of the planet to the object being launched.
G is a universal constant called the gravitational constant (6.67-10-" ).
kg-s
Notice that the potential energy is 0 when you are infinitely far away from the
planet, and negative as you get closer.

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