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Which of newtons three laws states that momentum can be transferred between object but cannot be lost?
Just answer the question no comments please.
2 Answers
- RickBLv 77 years ago
It's a combination of the 2nd and 3rd Laws.
Imagine two objects A and B with masses Ma, Mb; and initial velocities Va and Vb.
When they collide, A exerts a certain force on B, call it "F_ab", for a certain time interval t. This causes B to change its velocity by a certain amount ΔVb. The acceleration of B is therefore (by definition) ΔVb/t, and by Newton's 2nd Law:
F_ab = (Mb)(ΔVb/t)
or:
(F_ab)t = (Mb)(ΔVb)
But note that (Mb)(ΔVb) is just the change in B's momentum, which we can call ΔPb:
(F_ab)t = ΔPb
By a completely analogous argument, if F_ba is the force that B exerts on A, and if ΔPa is the change in A's momentum, then:
(F_ba)t = ΔPa
But Newton's 3rd Law states that F_ab = −F_ba. Apply this to the two equations above and you get:
ΔPb = −ΔPa
Which is another way of saying: The amount of momentum gained by one object equals the amount gained by the other object. Another way to put it is:
Overall change in momentum = ΔPa + ΔPb
= ΔPa + (−ΔPb)
= 0
That is, the overall change in momentum is zero. In the system as a whole, no momentum is gained or lost; only transferred from one object to another.