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ehrenfest
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Homework Statement
The book I am using (Zwiebach on page 66) uses the expression
[tex] hello [/tex]
[tex] dF_v = T_0 \frac{ \partial{y}{\partial{x}} |_{x+dx} -T_0 \frac{ \partial{y}{\partial{x}} |_{x} [/tex]
A net force on an infinitesimal string is the sum of all the forces acting on the string. This includes both external forces, such as tension or gravity, and internal forces, such as friction. The net force determines the acceleration of the string.
The net force on an infinitesimal string can be calculated by adding up all the individual forces acting on the string. These forces can be calculated using Newton's second law, which states that force equals mass times acceleration (F=ma). In the case of an infinitesimal string, the mass is assumed to be negligible, so the net force is simply equal to the acceleration of the string.
The net force on an infinitesimal string is significant because it determines the motion of the string. If the net force is zero, the string will remain at rest or continue to move at a constant velocity. If the net force is non-zero, the string will accelerate in the direction of the net force.
Tension is one of the external forces that can contribute to the net force on an infinitesimal string. If the string is being pulled from both ends, the tension forces will cancel each other out and the net force will be zero. However, if there is an imbalance in the tension forces, there will be a net force on the string, causing it to accelerate.
Yes, the net force on an infinitesimal string can be negative. This means that the forces acting on the string are in opposite directions and the string will experience a deceleration. A negative net force can also indicate that the string is being pulled in one direction and pushed in the opposite direction, resulting in a net force of zero but a change in the direction of motion.