2 masses and 2 pulleys (Kleppner and Kolenkow)

In summary, the conversation discusses an issue with the constraint equation for the total length of strings, and the need for an explanation for the division by 2 in the equation. The speaker also mentions that the equation does not represent the total length of the strings, but represents a fixed quantity. They suggest identifying what this quantity represents and clarify if the variable "a" was treated as a constant when taking the time derivative of the first equation.
  • #1
AspiringPhysicist12
16
6
Homework Statement
Masses M1 and M2 are connected to a system of strings and pulleys as shown. The strings are massless and inextensible, and the pulleys are massless and frictionless. Find the acceleration of M1.
Relevant Equations
x_1 + L_1 + L'_1 + (x_2 + L_2 + L'_2)/2 = constant C
For the official answer, I would appreciate an explanation as to why there's a division by 2 in the constraint equation for the total length of the strings, and why the way I wrote my constraint equation is incorrect.
 

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  • #2
AspiringPhysicist12 said:
For the official answer, I would appreciate an explanation as to why there's a division by 2 in the constraint equation for the total length of the strings,
Their constraint equation does not represent the total length of the strings. But it does represent a certain fixed quantity. Try to identify what it represents.
 
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  • #3
1598455060739.png


When you took the time derivative of the first equation, did you treat ##a## as a constant?
 

1. How does the tension in the strings change when the masses are moved?

The tension in the strings will change depending on the direction and magnitude of the movement of the masses. When one mass is moved up, the tension in the string connected to that mass will increase, while the tension in the other string will decrease. When both masses are moved in the same direction, the tension in both strings will increase. When the masses are moved in opposite directions, the tension in one string will increase while the tension in the other string will decrease.

2. What is the relationship between the masses and the acceleration of the system?

The acceleration of the system is directly proportional to the difference in mass between the two masses. This means that if the masses are equal, the acceleration will be zero. As the mass of one of the objects increases, the acceleration of the system will also increase. This relationship can be described by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

3. How does the direction of motion of the masses affect the acceleration of the system?

The direction of motion of the masses does not affect the acceleration of the system. As long as the masses are connected by a string and the strings are attached to fixed points, the acceleration of the system will remain the same regardless of the direction of motion of the masses. This is because the forces acting on the masses are always in opposite directions, canceling each other out and resulting in a net force of zero.

4. Can the masses be at rest while the system is in motion?

Yes, it is possible for the masses to be at rest while the system is in motion. This can happen when the masses are equal and the strings are at an angle of 90 degrees from each other. In this case, the tensions in the strings will cancel out and the net force on the masses will be zero, resulting in no acceleration. However, if the masses are unequal or the strings are at different angles, the system will experience some acceleration even if the masses are at rest.

5. What is the significance of the pulleys in this system?

The pulleys in this system serve to redirect the forces and change the direction of motion of the masses. Without the pulleys, the system would not function as a simple machine and the forces would act in the same direction, resulting in no net force and no acceleration. The pulleys also allow for multiple masses to be connected and moved simultaneously, making it a useful tool for studying the principles of mechanics.

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