consider two asymptotic behaviors, what will happen if the two masses are equal to each other, that is, m1=m2?
As a second matter of interest, what if one of the masses is much larger than the other: m1 >> m2?
in regards to an atwood's machine. i don't understand what i'm supposed to do here...
The acceleration of the masses in an Atwood's machine is
a = g*(m1-m2)/(m1+ m2)
As m1 -> m2' , a approaches zero.
If m2 >> m1, a --> g
In an Atwood's machine, two masses are connected by a string or a rope that passes over a pulley. The behavior of the system depends on the relative values of the two masses. Let's consider the two cases you mentioned.
1. If the two masses are equal (m1 = m2), the system will be in equilibrium. Since the masses are the same, there will be no net force acting on the system, and it will remain stationary. In this case, the tension in the rope will also be equal on both sides of the pulley.
2. If one of the masses is much larger than the other (m1 >> m2), the system will exhibit a different behavior. The larger mass will exert a much greater force than the smaller mass, causing it to accelerate downwards. The smaller mass will, in turn, accelerate upwards. The system will continue to accelerate until the forces become balanced, at which point it will reach a state of equilibrium.
To analyze the system further, you can use Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it. By considering the forces acting on each mass and using this equation, you can determine the relationship between the masses and their resulting accelerations.
Remember, understanding the physical principles and equations involved is essential in comprehending the behavior of Atwood's machines. So, it's important to familiarize yourself with concepts like Newton's laws of motion and the equations related to them.