Newton's 2nd Law: Conditions & Application

[semc]

hmm...i was wondering is there any conditions for the use of Newton's second law?

 

[Doc Al]

What do you mean?

 

[radou]

hmm...i was wondering is there any conditions for the use of Newton's second law?

The 'conditions' which imply the usage of an equation are read from the equation itself.

 

[semc]

i don't reali know how to put it in words but erm...we do not need a varying mass to use F=dmv/dt right?

 

[Doc Al]

Right. F= d(mv)/dt is more general than F=ma, which assumes a non-varying mass.

 

[radou]

i don't reali know how to put it in words but erm...we do not need a varying mass to use F=dmv/dt right?

Well, if the mass is not constant, then you have $$\vec{F}=\frac{d}{dt}(m\vec{v})=\frac{dm}{dt}\vec{v}+m\frac{d\vec{v}}{dt}$$.

 

[semc]

Alright i just came across this dumb conditions and i wanted to verify that this is nonsense Thanks

 

[OlderDan]

Well, if the mass is not constant, then you have $$\vec{F}=\frac{d}{dt}(m\vec{v})=\frac{dm}{dt}\vec{v}+m\frac{d\vec{v}}{dt}$$.

An easy calculus problem, but a tricky physics problem. Suppose there is a railroad car coasting with speed V on a straight horizontal track without any rolling friction. The car is full of water and has initial mass Mo and velocity Vo. As the car rolls, the water in the tank leaks out of a hole in the bottom of the tank at a rate we can assume to be constant (maybe the hole gets a little bigger as the water level drops). So the mass M of the car is changing at a constant rate. The only forces acting on the car are gravity and the normal force, both of which are perpendicular to the motion. What happens to the velocity of the car?