Force applied to dumbbell to CM and edge

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Discussion Overview

The discussion centers on the effects of applying a force to a dumbbell at different points—specifically at its center of mass versus at its edge. Participants explore the implications for momentum, energy, and motion, including concepts of torque and rotational dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that applying a force at the center of mass and at the edge results in the same center of mass velocity due to the impulse imparted, but questions the energy implications of these two scenarios.
  • Another participant explains that while the impulse (change in momentum) is the same in both cases, the energy is greater when the force is applied at the edge due to the additional distance over which the force acts.
  • A later reply suggests that it is challenging to apply the same force at the end of the dumbbell as at the center because the end begins to spin, potentially affecting the impulse applied.
  • One participant emphasizes that energy gain is dependent on the distance over which the force is applied, rather than the duration of the application.
  • There is a repeated concern about whether the same force and time are truly applied in both scenarios, highlighting uncertainty in the experimental setup.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between force application, energy, and motion, indicating that the discussion remains unresolved with multiple competing perspectives on the mechanics involved.

Contextual Notes

Participants acknowledge the complexity of measuring force application consistently across different points on the dumbbell, which may affect the conclusions drawn about energy and motion.

Malabeh
Today in class we learned about how if a force F is applied to a dumbbell on its center of mass and then separately applied to the edge where it gets its maximum torque, the dumbbell will have the same CM velocity after. It makes sense when you think about it in terms of momentum. F times T gives the impulse and so it is the same in both cases. I get confused about its energy. The second case has more energy because it is rotating and translating...makes sense, BUT how can a force applied for a certain time give something more energy when it is applied to a different position? Also, in my mind I imagine the force being applied to the dumbbell in case 2 and it just rotates around that point because there is maximum torque. Obviously my thoughts are flawed, would anyone care to explain why? If you can provide mathematical proof that'd be great!
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EDIT: If I flick my pen at its center of mass, it goes across the table really fast, but if I flick it at the end, it spins and only has a minor transnational velocity. That seems counter intuitive to what my teacher said.
 
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Change in momentum is given by impulse. Impulse is the integral of force over time. Change in energy is given by work. Work is the integral of force over distance.

The end of the dumbbell moves relative to the center of mass. If you apply the same force for the same time at the end of the dumbbell rather than at the center, you will have imparted the same impulse. But you will have imparted more energy because of that additional movement.
 
Malabeh said:
EDIT: If I flick my pen at its center of mass, it goes across the table really fast, but if I flick it at the end, it spins and only has a minor transnational velocity. That seems counter intuitive to what my teacher said.
It's not so easy to flick the end of the pen with the same force as you can flick the center of mass, since the pen starts spinning and the point of contact moves away from you more quickly. When flicking the center you are probably exerting a greater impulse--more force for a greater time.
 
Malabeh said:
BUT how can a force applied for a certain time give something more energy
Because energy gain depends on the distance the force is applied over, not the duration it is applied for.

Malabeh said:
If I flick my pen at its center of mass, it goes across the table really fast, but if I flick it at the end, it spins and only has a minor transnational velocity. That seems counter intuitive to what my teacher said.
How can you be sure you applied the same force over the same time in both cases?
 

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