# Springs Newton's laws of motion diatomic molecules

I was asked to explain why both molecules hydrogen and iodine experience the same force when they oscillate in Simple harmonic motion using Newton's third law, but I cannot seem to justify my explanation.

I said that because the molecules are attached to the same spring, the Iodine and Hydrogen molecules experience the same tension, although apparently this explanation is does not use Newton's third law.

• So you were told that this system didn't follow Newton's Third Law, but you weren't told why? – probably_someone Jun 28 '17 at 16:07
• @probably_someone no I was told it does follow newton's third law, but my reasoning doesn't use newton's third law at all – vik1245 Jun 28 '17 at 16:11

Suppose we work in the centre of momentum frame i.e. the frame where the total momentum is zero. In this frame the momenta of the two atoms must be equal and opposite i.e.

$$p_H = -p_I$$

If we differentiate wrt to time we get:

$$\frac{dp_H}{dt} = -\frac{dp_I}{dt}$$

And of course the rate of change of momentum with time is just the force, so we get:

$$F_H = -F_I$$

The minus sign is there because the forces on the two atoms are in opposite directions. Newton's third law creeps in because it's basically just a statement that total momentum is conserved.

• perfect thanks so much! uprate if you may find it useful for other people to look at! – vik1245 Jun 28 '17 at 17:45