How would you find the potential energy of just the string?JCOM44 said:How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it?
The string is uniform, so I know its center of mass is at L/2.
I tried using the fact that the only force on the string is F=mg, then W=mg*y, and remembering that -∇U=W, I found that U=-½mgy^2, but I feel this is not right because it has no information about the length, am I doing something wrong?phinds said:How would you find the potential energy of just the string?
Potential energy is defined with respect to some reference height. You have the masses of the rope and the weight, so you have two centers of mass to sum for the total GPE. But each has to be some distance above the ground (if that's where you are taking GPE=0 to be), so when you do that sum, the length of the rope will come into play. Makes sense?JCOM44 said:I tried using the fact that the only force on the string is F=mg, then W=mg*y, and remembering that -∇U=W, I found that U=-½mgy^2, but I feel this is not right because it has no information about the length, am I doing something wrong?
JCOM44 said:How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it? The string is uniform, so I know its center of mass is at L/2.
Potential energy of a massive string refers to the stored energy in a string that is under tension or stretched.
The potential energy of a massive string is calculated using the formula PE = ½kx², where k is the string's stiffness coefficient and x is the displacement of the string from its equilibrium position.
The potential energy of a massive string is affected by two main factors: the stiffness of the string (determined by the material and thickness) and the displacement of the string from its equilibrium position.
Yes, potential energy of a massive string can be converted into other forms of energy, such as kinetic energy, when the string is released and the stored energy is released as motion.
The potential energy of a massive string is directly related to the work done on the string. Work is done on the string when it is stretched or compressed, increasing its potential energy. When the string is released, the potential energy is converted into work and the string returns to its equilibrium position.