Help with gravity Question

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In summary, to have 1/100 of its normal weight, a rocket should be 9 Earth radii above the surface of the Earth. This can be found by taking the square root of 100 and multiplying it by the initial distance from the Earth's center, or by multiplying the initial distance by 10 and subtracting 1. The key is to understand that the weight of an object is inversely proportional to the square of its distance from the center of the Earth.
  • #1
Stratosphere
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Homework Statement


How high above the surface of the Earth should a rocket be
in order to have 1/100 of its normal weight? Express your answer
in units of Earth radii.


Homework Equations


F=GMm/r2
F=mg


The Attempt at a Solution


r = √(( 6.67 x 〖10〗^(-11) x 5.97 x 〖10〗^24 )/0.098)
then divide by 6.37*106

I asked for help from one of my friends and he emailed me this but I think he might have messed somthing up. I keep getting a really big number.

I also know the answer its 9 radii but i don't understand how to get that answer.
 
Last edited:
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  • #2
You don't need to use the actual mass of the Earth or the value of G.

You know that the weight is F = GMm/r^2
You know 'GMm' doesn't change,
So all you are asking is what do you have to do to 'r' to make 'r^2' 1/100 as big

ps. Careful with the final answer, r is from the centre of the Earth but the question asks for height above surface.
 
Last edited:
  • #3
So i have to make r^2=1/10 of r^2?
 
  • #4
yes - it migth help to label them rinitial and rfinal to avoid confusing yourself !
 
  • #5
so how do i do that i tried r^2/10 its not right.
 
  • #6
i think i got it, so I did r*10 then subtract 1 to get distance from Earth's surface not its center. Thnx for the help.
 
  • #7
More formally you would write
ri2 = 100 rf2

Take square root of both sides, it also helps to know that sqrt(ab) = sqrt(a) * sqrt(b)
 

1. What is gravity and how does it work?

Gravity is a fundamental force of nature that is responsible for the attraction between objects with mass. It works by pulling objects towards each other and is affected by the mass and distance between the objects.

2. Why do objects fall when dropped?

Objects fall when dropped because of the force of gravity. The Earth's mass creates a gravitational field that pulls objects towards its center. As a result, objects closer to the surface, like when they are dropped, experience a greater force of gravity and fall towards the ground.

3. How is gravity related to mass and weight?

Mass and weight are both related to gravity. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on that object. The greater the mass of an object, the more gravitational force it exerts and the more weight it has.

4. Can gravity be turned off or canceled out?

No, gravity is a fundamental force that cannot be turned off or canceled out. It exists everywhere in the universe and is constantly exerting its force on objects with mass.

5. How does gravity affect the motion of objects in space?

Gravity plays a key role in the motion of objects in space. It is responsible for keeping planets in orbit around the sun and moons in orbit around planets. The strength of gravity decreases with distance, so the farther an object is from a large mass, the weaker the gravitational force it experiences.

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