Astronaut releasing apple - Find acceleration

[dance_sg]

Homework Statement

In a space shuttle orbiting 6.40 x 103 km above the surface of Earth, an astronaut releases
a 325 g apple. If the radius of Earth is 6.40 x 103 km, what is the acceleration of the apple?

A. 2.45 m/s2
B. 4.90 m/s2
C. 9.80 m/s2
D. 19.6 m/s2

Homework Equations

g=GM/r^2

The Attempt at a Solution

i converted grams to kg whihc gave me 0.325kg. then i multiplied that number by the universal gravitational constant. then i divided that number by two times the radius. what am i doing wrong?

 

[kuruman]

Homework Statement

In a space shuttle orbiting 6.40 x 103 km above the surface of Earth, an astronaut releases
a 325 g apple. If the radius of Earth is 6.40 x 103 km, what is the acceleration of the apple?

A. 2.45 m/s2
B. 4.90 m/s2
C. 9.80 m/s2
D. 19.6 m/s2

Homework Equations

g=GM/r^2

The Attempt at a Solution

i converted grams to kg whihc gave me 0.325kg. then i multiplied that number by the universal gravitational constant. then i divided that number by two times the radius. what am i doing wrong?

What did you use for the radius? It should be the distance from the center of the Earth not the distance above the surface of the Earth.

 

[Pengwuino]

Two times the radius? Do you mean the radius squared? 2 x R is not hte same as R^2, which is R * R.

 

[ideasrule]

And also, "M" is Earth's mass, not the apple's mass. Think about it: gravitational acceleration does not depend on mass.

 

[dance_sg]

sorry yes, i meant the radius squared. and so the Earth's mass is 5.97 x 10^24, but don't i need to use the mass of the apple at all?

 

[Pupil]

sorry yes, i meant the radius squared. and so the Earth's mass is 5.97 x 10^24, but don't i need to use the mass of the apple at all?

F = ma

Fg = GMm/r^2

GMm/r^2 = ma <--- Cancel little m.

GM/r^2 = a

 

[dance_sg]

so 6.67 x 10^-11 (0.325)/6.40 x 10^3^2. that gives me some huge big number like 5.29 x 10^ -19 and that is not one of the options.

 

[dance_sg]

even when i use Earth's mass (5.97 x 10^ 24) it still gives me a huge number.

 

[rock.freak667]

even when i use Earth's mass (5.97 x 10^ 24) it still gives me a huge number.

r=2R

so g=GM/4R²

That shouldn't give you that big of a number

 

[bm0p700f]

You need to make sure r is in m not km then it will work.

 

[dance_sg]

so u guys gave me two equations: g=GM/4R2, GM/r^2 = a. which one is right? and thanks bm0p700f for telling me to convert!

 

[Pupil]

so u guys gave me two equations: g=GM/4R2, GM/r^2 = a. which one is right? and thanks bm0p700f for telling me to convert!

The former equation is an application of the latter equation. The distance from the center of the Earth to the ground is R. The distance from the ground to the satellite is R. R + R = 2R. 2R is the thing getting squared in the denominator. Distinguish between the capital Rs and the lower case rs. Think of the lower case r as the general distance, and the big R as an actual measurement.