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Fascheue
What types of objects does Newtonian mechanics deal with? Is it just rigid bodies? I’m not sure how Newton’s laws could explain something like the motion of a wiggling rope.
Isn’t that too complicated to be useful though? Or is the only way to find something like the complicated motion of a rope with simulations on a computer?anorlunda said:It may not seem obvious, but Newtonian mechanics to apply to a rope.
To make is easier to visualize, imagine it as a wiggling chain. Each link is a rigid body and you can use Newton's laws in their familiar form. Make the link size arbitrarily small and you have a continuous rope. The physical laws don't change with link size.
Finite Element Analysis is probably too clunky to use on such a problem -- possible, but inefficient. One could make simplifying assumptions so that the differential equations are tractable. That's still Newtonian physics.Fascheue said:Isn’t that too complicated to be useful though? Or is the only way to find something like the complicated motion of a rope with simulations on a computer?
Newton's first law states that an object will remain at rest or in constant motion unless acted upon by an external force. In the case of a wiggling rope, the rope will continue to move back and forth with a constant frequency and amplitude unless an external force, such as tension from the person wiggling it, is applied.
Newton's second law, also known as the law of acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In the case of a wiggling rope, the amount of force applied by the person wiggling it will determine the rope's acceleration and how much it will bend and wiggle.
The tension in a rope is directly related to the rope's motion. When a rope is wiggled, tension is created as the rope is pulled in opposite directions. This tension causes the rope to bend and wiggle, and the magnitude of the tension will determine the amplitude of the wiggles.
Yes, a wiggling rope can exhibit harmonic motion, which is a type of motion where the restoring force is directly proportional to the displacement from equilibrium. In the case of a wiggling rope, the tension in the rope acts as the restoring force, and the frequency and amplitude of the wiggles can be controlled to create harmonic motion.
The length and thickness of a rope can affect its motion when wiggled in several ways. A longer and thicker rope will have a higher mass and therefore require more force to move. Additionally, a longer and thicker rope will also have a lower natural frequency, meaning it will take longer for the rope to complete one full wiggle. These factors can impact the amplitude and frequency of the wiggles in the rope's motion.