Change in gravitation potential energy in space

  • #1
217
0

Homework Statement


an object of mass 750 kg is lifted from the earth's surface to a height of 6.8 x 10^6 m above its surface. Calculate the change in gravitational potential energy for the object.


The Attempt at a Solution



I used this formula ΔEg = Eg2 - Eg1
ΔEg = -(GMm/r2) - (-GMm/r1)

Eg2 = -(GMm/r2)
Eg2 = -(6.67x10^-11 Nm^2/kg^2)(5.98 x10^24kg)(750kg)/(6.8x10^6m)+(6.37x10^6m)
Eg2 = -2.27 x 10^10 J

Eg1 = -(GMm/r1)
Eg1 = -(6.67x10^-11 Nm^2/kg^2)(5.98 x10^24kg)(750kg)/(6.37x10^6m)
Eg1 = -4.7x 10^10 J

ΔEg = Eg2 - Eg1
ΔEg = -2.27 x 10^10 J + 4.7x 10^10 J
ΔEg = 2.43 x 10^10 J

Is my process correct?
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
37,159
7,276
Yes. But do be careful with parentheses: /(6.8x10^6m)+(6.37x10^6m):wink:
 
  • #3
217
0
Yes. But do be careful with parentheses: /(6.8x10^6m)+(6.37x10^6m):wink:

Is in like when im adding them?
Are all the calculation right.. i really had trouble with them...
like adding the exponents above the 10... :frown:
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
37,159
7,276
Is in like when im adding them?
Most likely you knew what you intended when you wrote /(6.8x10^6m)+(6.37x10^6m), and therefore treated it as /((6.8x10^6m)+(6.37x10^6m)) when you used it, but it's confusing for others (including examiners!), and might confuse you sometime.
I did a sanity check. The altitude doubled the radius, and then some, so the energy should halve, and then some - which it did.
 
  • #5
217
0
Most likely you knew what you intended when you wrote /(6.8x10^6m)+(6.37x10^6m), and therefore treated it as /((6.8x10^6m)+(6.37x10^6m)) when you used it, but it's confusing for others (including examiners!), and might confuse you sometime.
I did a sanity check. The altitude doubled the radius, and then some, so the energy should halve, and then some - which it did.
so it is correct?
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
37,159
7,276
I believe so, but I did not check the arithmetic in detail.
 

Related Threads on Change in gravitation potential energy in space

Replies
9
Views
15K
Replies
3
Views
5K
Replies
1
Views
8K
Replies
1
Views
2K
  • Last Post
Replies
19
Views
2K
Replies
3
Views
825
Replies
5
Views
9K
Replies
7
Views
2K
Replies
5
Views
5K
E
Replies
3
Views
6K
Top