• Support PF! Buy your school textbooks, materials and every day products Here!

Help with Energy unit Joules EASY

  • #1
[SOLVED] Help with Energy unit ... Joules... EASY!!!

Homework Statement



The sun burns up 3.6 x 10[tex]^{9}[/tex] kg of matter each second.
Using the formula E = mc[tex]^{2}[/tex], determine how much energy the
sun releases each second. [Speed of light: 3 x 10[tex]^{8}[/tex] m[tex]/[/tex]s]


Homework Equations



E = mc[tex]^{2}[/tex]


The Attempt at a Solution



E = mc[tex]^{2}[/tex]
. .= (3.6 x 10[tex]^{9}[/tex] kg)(3 x 10[tex]^{8}[/tex] m[tex]/[/tex]s)[tex]^{2}[/tex]
. .= (3.6 x 10[tex]^{9}[/tex] kg)(9 x 10[tex]^{16}[/tex] m[tex]^{2}[/tex][tex]/[/tex]s[tex]^{2}[/tex])
. .= 32.4 x 10[tex]^{25}[/tex] [tex]\frac{kg \cdot m^2}{s^2}[/tex]



Now I'm stumped with what to do with the units... I know it should be Joules per second. But how do I show in my solution that Joules will come out? Joules is N[tex]\cdot[/tex]m!!!

Do I have to change the kg into N? .... My textbook says that the magnitude of c[tex]^{2}[/tex] is 9 x 10[tex]^{16}[/tex] Joules per kilogram.

Please check my calculations also!!!
Thank You!!! :smile:
 

Answers and Replies

  • #2
malawi_glenn
Science Advisor
Homework Helper
4,786
22
First hint: How is "Joule" defined?
Second hint: If E = mc[tex]^{2}[/tex] is valid, and you have SI units to the right, then you must obtain SI units on the left hand side as well.

The second hint would not be true if you was working with the natural units in sub-atomic phyiscs, where both c and h-bar = 1 i.e E = m, then one must do a more careful unit analysis.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,777
911
A Joule is N m and a Newton, N, is kg m/s2. So a Joule is kgm2/s2. That's exactly what you have!
 
  • #4
Hmmm.....

well Joule is the unit of work. N*m
Newton x meter
 
  • #5
A Joule is N m and a Newton, N, is kg m/s2. So a Joule is kgm2/s2. That's exactly what you have!

So that's understood? I'll then just add....

E = mc[tex]^{2}[/tex]
. .= (3.6 x 10[tex]^{9}[/tex] kg)(3 x 10[tex]^{8}[/tex] m[tex]/[/tex]s)[tex]^{2}[/tex]
. .= (3.6 x 10[tex]^{9}[/tex] kg)(9 x 10[tex]^{16}[/tex] m[tex]^{2}[/tex][tex]/[/tex]s[tex]^{2}[/tex])
. .= 32.4 x 10[tex]^{25}[/tex] [tex]\frac{kg \cdot m^2}{s^2}[/tex]
. .= 32.4 x 10[tex]^{25}[/tex] Joules

Simple as that?
Yipee! :biggrin:

Are my calculations correct? exponents....
 
  • #6
malawi_glenn
Science Advisor
Homework Helper
4,786
22
Yes, since F [N] = m*a [kg * m/s^2 ]
 

Related Threads for: Help with Energy unit Joules EASY

Replies
16
Views
4K
  • Last Post
Replies
7
Views
2K
Replies
10
Views
3K
  • Last Post
Replies
1
Views
1K
Replies
7
Views
1K
Replies
2
Views
18K
  • Last Post
Replies
2
Views
775
  • Last Post
Replies
5
Views
1K
Top