The discussion centers on the application of the conservation of string principle in a physics problem involving a symmetric sub-pulley system. Participants emphasize the importance of establishing equations that relate the lengths of string sections to the heights of the masses involved. Key equations include the relationship between the vertical positions of the masses and the center of the pulley, leading to the conclusion that the acceleration of the left mass is the negative average of the accelerations of the right two masses. The discussion highlights the necessity of differentiating these relationships to derive velocity and acceleration equations.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics and dynamics, as well as educators seeking to enhance their understanding of pulley systems and conservation principles.
The sub-pulley is symmetric, correct? That is, there is no difference between its right and left hand sides? They are mirror images of each other?mancity said:
I take the masses as unknown.jbriggs444 said:
Write equations relating string (section) lengths to heights of masses, throwing in constants as necessary. Differentiate twice.mancity said:
'Conservation of string' is an unusual way to state that the length of the string is constant. So when you set up a set of equations for your exercise, one of them is a relationship betweenmancity said:
Relative to the bottom pulley, the average acceleration of the bottom two masses is zero. The acceleration of the upper mass is minus the acceleration of the bottom pulley.mancity said:
My impression is that the OP has been instructed to use conservation of string length to obtain the result. That suggests to me applying your framework to positions and then differentiating.Chestermiller said:
