How does impulse relate to energy when the net force is zero?

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Discussion Overview

The discussion revolves around the relationship between impulse and energy in scenarios where the net force acting on an object is zero. Participants explore concepts related to work, energy expenditure during static actions, and the implications of applying force without resulting motion.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that when holding an object still, the work done is zero due to no displacement, yet they calculate an impulse based on the force applied over time.
  • Another participant questions the source of energy expenditure when no mechanical energy changes occur, suggesting that energy could be accounted for in other forms.
  • A different participant proposes that the energy spent during static actions is converted into heat, drawing parallels to energy loss in braking systems.
  • One participant introduces the idea that energy may also go into deforming the wall when force is applied, suggesting a different perspective on energy transfer.
  • There is a discussion about whether the energy spent during actions that do not result in work is primarily dissipated as heat.
  • A participant likens the wall to a super-stiff spring, indicating a conceptual analogy in understanding energy transfer during force application.

Areas of Agreement / Disagreement

Participants express differing views on the nature of energy expenditure when no work is done. While some suggest it primarily converts to heat, others introduce alternative explanations, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants reference concepts such as impulse, work, and energy without fully resolving the implications of these relationships, leaving some assumptions and definitions open to interpretation.

eohjelle
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Work is defined as force times displacement. When the force is applied on an object which does not move, or is applied perpendicular to the direction of motion, the work done is zero.

So let's say I hold an object with a mass of 1 kg still in the air for 10 seconds. Because the object does not move, Newton's first law tells me that ƩF=0. Which means that I apply a force which is of the same magnitude and opposite direction of the force applied by gravity. The work done by me is zero because the object does not move. The net impulse on the object is also zero, because the momentum of the object does not change. However, the impulse done by me is I = Ft = mgt = 1*9.81*10 kgm/s = 98 kgm/s.

When holding the object, the energy it feels like I'm spending is closely related to impulse: magnitude of the force that I have to apply and for how long.

When I hold my hands still in the air, or push against a wall, no work is done. However, I clearly spend energy while doing these activities. Where does this energy go?
 
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The potential and kinetic energies didn't change in that ball, so mechanical energy is out. What other energy could you have? I mean unless you want to get really nitty gritty
 
eohjelle said:
Where does this energy go?
Heat. Similarly, if you stomp on the brakes and rev your engine you can waste a lot of energy without doing any work. It goes to heat there too.
 
eohjelle said:
When I hold my hands still in the air, or push against a wall, no work is done. However, I clearly spend energy while doing these activities. Where does this energy go?

It goes partly into deforming the wall

eohjelle said:
When the force is applied on an object which does not move...

Everything moves :)
 
@Woopydalan That's the point. I didn't change the kinetic or potential energy of the ball, but I still spent energy.

@DaleSpam So what you're saying is that when you don't do any work it all just goes to heat?

@afreiden A-ha. So a wall is kind of like a super-stiff spring?
 
eohjelle said:
@DaleSpam So what you're saying is that when you don't do any work it all just goes to heat?
Yes, almost always.
 

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