Two Masses Connected by a Pulley

[brentd49]

I have a general question about how to apply Newton's Second Law. When we write Fnet=ma, I am sometimes unsure of myself what the 'm' is in the problem.

For instance, when two masses (m1 and m2) are connected by a pulley is 'm' equal to m1+m2, or just the mass of interest?

How can I be absolutely sure of myself when I am solving problems using Newton's Second Law?

Does this have something to do with the technique of cutting (i.e. if two people are pulling opposite ends of a rope, then by cutting the rope, one can find the rope's tension.)?

 

[cepheid]

How can I be absolutely sure of myself when I am solving problems using Newton's Second Law?

Newton's second law says that the net force acting on an object is equal to that object's mass times its acceleration.

Just be sure that you know which net force you are calculating, i.e. which object you are applying Newton's second law to. If Fnet refers to the net force on mass 1, then it is given by m1 * a1, by Newton's second law. If it refers to the net force on mass 2, then it is given by m2 * a2.


If you include both masses (and assume the rope has negligible mass), then you are calculating the net force on the system, and have to be sure to multiply this mass by the acceleration of the system, which is...?

 

[quicknote]

Thank you for your question. When using Newton's Second Law, the 'm' in the equation refers to the total mass of the system. In the case of two masses connected by a pulley, the total mass would be the sum of both masses (m1 + m2). This is because the acceleration of the system is dependent on the total mass, not just one individual mass.

To be absolutely sure when solving problems using Newton's Second Law, it is important to clearly define the system and all the forces acting on it. This includes identifying the total mass of the system and any external forces acting on it.

The technique of cutting a rope can be helpful in determining the tension in a system, but it is not directly related to Newton's Second Law. Instead, it is a way to analyze the forces acting on a specific object in a system.

I hope this helps clarify any confusion you may have had about applying Newton's Second Law. Remember to always carefully consider the system and all the forces acting on it to ensure accurate solutions.