Concept explainers
A meteor starts from rest at a very great distance from the earth. Knowing that the radius of the earth is 6370 km and neglecting all forces except the gravitational attraction of the earth, determine the speed of the meteor (a) when it enters the ionosphere at an altitude of 1000 km. (b) when it enters the stratosphere at an altitude of 50 km. (c) when it strikes the earth’s surface.
(a)
Speed of meteor.
Answer to Problem 13.36P
Speed of meteor is, v=10.39 km/s.
Explanation of Solution
Given information:
Initially start from rest.
Radius of earth (R) = 6370 km.
When it enters at ionosphere at an altitude of 1000km.
Calculation:
From work energy principle for a meteor,
Where, F is gravitational force and given as
So, work energy equation
Integrate the equation from o to v and 0 to x.
This is the equation for velocity of the meteor.
For x=6370km+1000 km=7370km
(b)
Speed of meteor
Answer to Problem 13.36P
Speed of meteor is, v = 11.137 km/s.
Explanation of Solution
Given information:
Initially start from rest.
Radius of earth (R) = 6370 km.
When it enters at ionosphere at an altitude of 50km.
Calculation:
From work energy principle for a meteor
Where, F is gravitational force and given as
Where, R radius of earth, r distance travel by the meteor and m mass of the meteor.
So, work energy equation
Integrate the equation from o to v and 0 to x.
This is the equation for velocity of the meteor.
For x=6370km+50 km=6420 km
(c)
Speed of meteor.
Answer to Problem 13.36P
Speed of meteor when it strike to the earth is, v=11.18 km/s.
Explanation of Solution
Given information:
Initially start from rest.
Radius of earth (R) = 6370 km.
When it strikes to the earth.
Calculation:
From work energy principle for a meteor
Where, F is gravitational force and given as
Where, R radius of earth, r distance travel by the meteor and m mass of the meteor.
So, work energy equation
Integrate the equation from o to v and 0 to x.
This is the equation for velocity of the meteor.
For x=6370km+0 km=6370km,
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Chapter 13 Solutions
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