This discussion focuses on calculating the height a pendulum reaches after being pushed with a force of 10N at its equilibrium position. The key takeaway is that the energy increase from the applied force can be calculated by integrating the force over the displacement during the push. The conversation emphasizes that while an instantaneous force simplifies the problem, it is crucial to acknowledge that all forces have a non-zero application time, which can be approximated for calculations using formulas such as F=ma, v=at, and W=Fd. Additionally, the concept of impulse momentum is recommended for further understanding.
PREREQUISITESPhysics students, educators, and anyone interested in mechanics, particularly those studying pendulum dynamics and energy transfer in physical systems.
Integrate the force through the position displacement -- that will give you an energy increase, which you can translate into a higher zero velocity pause position. Makes sense?LightningBolt226 said:Usually, the pendulum problems I encounter relate to initial velocity. What happens if, at equilibrium, I push a pendulum with a certain amount of force? (E.g. 10N) Is there a way to calculate how high the pendulum will go? I guess it's complicated considering torque done by gravity, etc
It's a path integral, from the start of the push to the end of the push. How is the push force versus position defined in this problem? Is the push force constant over some arc length? Where on the pendulum is the push force applied?LightningBolt226 said:I'm not exactly sure what you mean. What are the limits of integration for this case?
That simplifies the problem a lot. But there is no such think as an instantaneous force. It can be applied over a small angle of the pendulum's travel, which makes the force*distance = change in energy approach a lot easier. Can you show us that math?LightningBolt226 said:Sorry, I forgot to mention earlier. Suppose that it was an instantaneous force that was applied. Also, suppose that the pendulum is a point mass and is where the force is applied.
There is no such thing as an instaneous application of force. It may not be very long, but there's always some non-zero time between the moment when we start applying the force and the moment when we stop.LightningBolt226 said:Sorry, I forgot to mention earlier. Suppose that it was an instantaneous force that was applied. Also, suppose that the pendulum is a point mass and is where the force is applied.