EL 1001 physics number 207... error?

[2010premed]

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The earth has a radius of approximately 6400 km. If an object could orbit the earth just at its surface, how fast would it have to trave?

supposed answer: 8 km/d

I'm getting the square root of whatever 64000 is...

 

[PiBond]

The earth has a radius of approximately 6400 km. If an object could orbit the earth just at its surface, how fast would it have to trave?

supposed answer: 8 km/d

I'm getting the square root of whatever 64000 is...

GMm/r^2 = mv^2/r

since it's just above the earth's surface, the r's cancel. mass of object also cancels

GM/r = v^2

(6.67e-11)(6e24)/(6400*1000) = v^2

v = 8000 m/s or 8km

 

[2010premed]

Why do you use that formula and not mg?

 

[PiBond]

Why do you use that formula and not mg?

we're dealing with centripetal acceleration caused my the gravitational force of earth. it's a pretty standard question dealing with our understanding of centripetal acceleration in a limiting case.

F = ma = GMm/r^2 = mv^2/r

 

[fizzgig]

near the earth's surface the force due to gravity IS mg right? so can't you use that?

mg = mv^2/r
sqrt(rg) = v
sqrt(6400000*10)=sqrt(64)*sqrt(1000000)=8*1000 = v (m/s)

 

[surag]

near the earth's surface the force due to gravity IS mg right? so can't you use that?

mg = mv^2/r
sqrt(rg) = v
sqrt(6400000*10)=sqrt(64)*sqrt(1000000)=8*1000 = v (m/s)

This also correct and ideally what u should use. I got same answer. I think op was confused by units. His answer would
be in meters. Converted to km he would have gotten right answer his way. Lol

 

[premed1001]

how do these answers make any sense? the question makes it sound like you have to find its tangiential speed, does it not? if it was traveling that fast with no tangiential speed it would crash into the earth, not orbit. what am i missing here??????

 

[notawonk]

The earth has a radius of approximately 6400 km. If an object could orbit the earth just at its surface, how fast would it have to trave?

supposed answer: 8 km/d

I'm getting the square root of whatever 64000 is...

I think the error may have come from units? try converting using all meters or all kilometers.

Meaning, use:
-a = v^2/r and use a = 10 m/s^2 (METERS, not km).
-use 64*10^5m for the radius
-then plug and chug for velocity
-answer will be 8*(10^3) METERS, or 8km.

Hope that helped!