Explain the relation btw 2nd law of motion to 3rd law
My initial reaction was to think that there was no relationship and that the laws are independent.
On consideration, I decided that there probabably is. I am starting to think that the second law says it all.
Newtons 2nd law definitely includes the first. The first law is about no forces acting and continuing with constant velocity. Put 0 into F=ma and you get 0 acceleration - which is constant velocity. So you can deduce the first law from the second.
Newtons second law was originally written in a form not like F=ma but more like F= rate of change of momentum F=(delta p)/ t. The word momentum did not exist in Newton’s time!
Now if there is no external force, there must be no change in momentum. Consider two bodies eg masses exerting a graviational force.
Consider the two bodies as one system- there is no outside force so the total momentum must remain unchanged. Newtons third law says that if one body experiences a force from another, the other body must experience an equal and opposite force (and for the same time!). So by the 2nd law - the change in momentum to one body is equal and opposite to the change in the other hence there is no change in momentum overall.
But I could have worked this out from the 2nd law- No outside force so total momentum must be unchanged. Either the bodies do not change momentum at all (No forces between them) or one body must increase its momentum by the same amount as the other decreases. This means that the impulse (Force x time) on one body must be eqaul and opposite to the impulse on the other. I think taking the times to be the same is obvious? So the two forces must be equal and opposite in direction.
In conclusion- Newton only really needed one law, the second. However, it terms of understanding, having laws one and three is very helpful. It is only much later when your understanding is more secure that you canstart to see that perhaps the other laws are not strictly necessary.
My initial reaction was to think that there was no relationship and that the laws are independent.
On consideration, I decided that there probabably is. I am starting to think that the second law says it all.
Newtons 2nd law definitely includes the first. The first law is about no forces acting and continuing with constant velocity. Put 0 into F=ma and you get 0 acceleration - which is constant velocity. So you can deduce the first law from the second.
Newtons second law was originally written in a form not like F=ma but more like F= rate of change of momentum F=(delta p)/ t. The word momentum did not exist in Newton’s time!
Now if there is no external force, there must be no change in momentum. Consider two bodies eg masses exerting a graviational force.
Consider the two bodies as one system- there is no outside force so the total momentum must remain unchanged. Newtons third law says that if one body experiences a force from another, the other body must experience an equal and opposite force (and for the same time!). So by the 2nd law - the change in momentum to one body is equal and opposite to the change in the other hence there is no change in momentum overall.
But I could have worked this out from the 2nd law- No outside force so total momentum must be unchanged. Either the bodies do not change momentum at all (No forces between them) or one body must increase its momentum by the same amount as the other decreases. This means that the impulse (Force x time) on one body must be eqaul and opposite to the impulse on the other. I think taking the times to be the same is obvious? So the two forces must be equal and opposite in direction.
In conclusion- Newton only really needed one law, the second. However, it terms of understanding, having laws one and three is very helpful. It is only much later when your understanding is more secure that you canstart to see that perhaps the other laws are not strictly necessary.
