Newton's 2nd Law: What is the Definition?

[jinhuit95]

I'm just curious about the second law. I was taught in secondary school that the definition of the 2nd law was just when a resultant force acts on an object with a constant mass, the object will accelerate and move in the direction of the resultant force. The product of the mass and the acceleration of the object is the resultant force. However, the definition of 2nd law I've learned is the rate of change of momentum is directly proportional to the net external force acting on the body and takes place in the same direction of the force. Which is correct??

 

[Chestermiller]

I'm just curious about the second law. I was taught in secondary school that the definition of the 2nd law was just when a resultant force acts on an object with a constant mass, the object will accelerate and move in the direction of the resultant force. The product of the mass and the acceleration of the object is the resultant force. However, the definition of 2nd law I've learned is the rate of change of momentum is directly proportional to the net external force acting on the body and takes place in the same direction of the force. Which is correct??

Both. They say exactly the same thing. The "net external force" is another name for the "resultant force." For constant mass, the rate of change of momentum is equal to the mass times the acceleration. In your second definition, the rate of change of momentum is more than just directly proportional to the net external force. It is equal to the net external force.

Chet

 

[D H]

The two forms, F=ma and F=dp/dt, are equivalent for constant mass systems. Arguing which is right in this context is an exercise of counting the number of angels that dance on the head of a pin.

They are anything but the same for a variable mass system. F=dp/dt becomes a frame-dependent quantity. In other words, F_ext is not well defined with this definition. People who work with variable mass systems inevitably use F=ma because this is a frame invariant quantity (ignoring relativistic effects, of course). This creates a different problem, which is the things we think of as "external forces" don't account for all of the acceleration. This problem is easily addressed by counting "thrust" (change in momentum due to expelled/accumulated mass) as an external force.