Talk:Calculus/Product Rule

Subsumed by the Calculus/Product and Quotient Rules page
The material from this page has been incorporated into the Calculus/Product and Quotient Rules page. Please direct your edits to that page instead of this one. Greenbreen (discuss • contribs) 07:38, 19 April 2011 (UTC)

Physics Example I: Rocket Acceleration
First of all, Newton's second law of motion is also true for model rockets. $$F = ma$$, whatever (nonrelativistic) object is considered.

To understand the error in this example one should consider the physical meaning of each equation.

$$p = mv$$: The impulse of an object is its mass times its velocity. Also, the impulse of a closed system is always conserved. But the impulse of a non-closed system or object, such as a rocket loosing mass is not conserved.

For example, if we set the effective force (thrust, gravity, etc.) to zero, where the "rocket" is just loosing mass without propulsion,the problem becomes obvious:

$$F=0= v\frac{dm}{dt} + m\frac{dv}{dt}$$

$$a = -\frac{v}{m}\frac{dm}{dt}$$

But there obviously cant be any acceleration since the net force on the rocket is zero, and its changing mass term does not mean that the momentum of the disappearing mass is transferred to the remaining mass of the rocket. --194.106.245.213 (discuss) 23:25, 10 October 2019 (UTC)