MEDAL GIVEN TO CORRECT ANSWER.
Which of the following are possible units for a spring constant?

A. J/nm
B. nm/J
C. N/nm
D. nm/N

Question

MEDAL GIVEN TO CORRECT ANSWER. 
Which of the following are possible units for a spring constant?

 		A.	J/nm
 		B.	nm/J
 		C.	N/nm
 		D.	nm/N

anonymous · Answer

Newton per nano meter (C). Look at the equation of Hooke's Law:

$$F=-Kx$$

where F is the force on the object attached to the spring, x is the displacement from the origin and K is the spring constant.

The unit of Force is Newtons, therefore the units on the right hand side of the equation must also equate Newtons. x is a length so can be metres, centimetres, nanometers etc..

Therefore, in order for the left hand side to equal newtons, K must be something that has length on the bottom of the unit:

$$K=\frac{ 1 }{ m }$$
 where m is metres.

This means the units for the entire equation goes something like this:

$$n=\frac{ n }{ m }m$$
where n is Newtons and m is metres. As you can see the m's cancel leaving newtons left on both sides.

anonymous · Answer

Indeed it is