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n0083
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Homework Statement
"Show how conservation of energy (with only gravitational potential energy and kinetic energy) can be gotten from Newton's Laws.
This was the question that was asked of me, and sorry for the wording not being terribly precise.
Homework Equations
I am not exactly sure which equations are allowed and which aren't.
I assume F=ma, but i am not sure about Fg = GmM/r^2, W=Fd, or kinematic equations.
By Newton's Laws do they mean more than the "three laws"?
The student had not studied calculus yet.
The Attempt at a Solution
For instance, if using (i) F=ma, (ii) vf^2=vo^2+2ad, and (iii) W=Fd, we can do the following:
i&ii) Fd = m(vf^2 - vo^2)/2 ==> Fd = (1/2)*m*vf^2 - (1/2)*m*vi^2
iii&previous) W = (1/2)*m*vf^2 - (1/2)*m*vi^2
But this required more than simply F=ma, nammely (ii) and (iii).
I read online that conservation of momentum can be derived from Newton's third law. How?
Newton's third law is not really an equation, but more of a 'concept'.
I am failing to understand something here.
Thanks for your help to discuss/answer this vague question,