Acceleration Due to Gravity on earth

In summary: The answer is correct but the units are wrong. You found H=2.732*Re. You used Re=6.37*10^6m so H=2.732*6.37*10^6m=17.34*10^6m=1.734*10^7m.
  • #1
eagles12
76
0

Homework Statement


At what altitude above the Earth's surface is the acceleration due to gravity equal to g/3?



Homework Equations



ag=G Me/(Re+H)^2

The Attempt at a Solution



I solved for H and got H=√3 Re-Re
using this i got 17*10^6
but it is saying this is not correct
 
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  • #2
eagles12 said:

Homework Statement


At what altitude above the Earth's surface is the acceleration due to gravity equal to g/3?



Homework Equations



ag=G Me/(Re+H)^2

The Attempt at a Solution



I solved for H and got H=√3 Re-Re
using this i got 17*10^6
but it is saying this is not correct
Can you show the details of your calculation? What value did you use for Re?
 
  • #3
eagles12 said:
I solved for H and got H=√3 Re-Re
using this i got 17*10^6
17*10^6 what? Distance isn't just a number. It has units. What are the units of this number 17*10^6, what units is the answer supposed to be in, and what value did you use for the radius of the Earth?
 
  • #4
for re i used 6.37*10^6m
the answer is also sopossed to be in meters

i started with ag=g Me/(Re+H)^2
then plugged in 1/3*9.8=G Me/(Re+H)^2
I reduced that to ag=1/(Re+H)^2=1/3(1/Re^2)
from there i got
(Re+H)^2=3Re^2
Re+H=sqrt(3)*Re
H=sqrt(3)Re-Re
 
  • #5
Your derivation looks okay, so you must be having finger problems with the calculator :smile:
 

1. What is acceleration due to gravity on earth?

Acceleration due to gravity on earth is the acceleration experienced by any object due to the gravitational force of the earth. It is denoted by the symbol 'g' and has an average value of 9.8 meters per second squared (m/s²).

2. How is acceleration due to gravity measured?

Acceleration due to gravity can be measured using a device called an accelerometer, which calculates the acceleration of an object by measuring its change in velocity over time. It can also be measured using the equation g = F/m, where F is the force of gravity and m is the mass of the object.

3. Does acceleration due to gravity change with altitude?

Yes, acceleration due to gravity does change with altitude. As an object moves further away from the earth's surface, the gravitational force decreases, resulting in a decrease in acceleration due to gravity. However, this change is very small and only becomes significant at extremely high altitudes.

4. How does acceleration due to gravity affect free-falling objects?

Acceleration due to gravity is responsible for the free-fall of objects towards the earth's surface. As an object falls, it accelerates at a rate of 9.8 m/s² due to the force of gravity. This acceleration continues until the object reaches its terminal velocity, which is when the upward force of air resistance equals the downward force of gravity.

5. Does acceleration due to gravity vary on different planets?

Yes, acceleration due to gravity varies on different planets depending on their mass and radius. The more massive and larger a planet is, the greater the gravitational force and therefore, the greater the acceleration due to gravity. For example, on the surface of the moon, the acceleration due to gravity is only 1.6 m/s², while on Jupiter it is 24.8 m/s².

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