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

In summary, work is defined as force times displacement, and when a force is applied on an object that does not move, or is applied perpendicular to the direction of motion, the work done is zero. Holding an object still in the air for 10 seconds involves applying a force equal in magnitude and opposite in direction to the force of gravity, resulting in zero work done. The net impulse on the object is also zero, but the impulse done by the person holding the object is not. The energy spent in this scenario is closely related to impulse and goes towards deforming the wall or creating heat. This also applies to activities like pushing against a wall or stomping on the brakes, where no work is done but energy is still expended, usually
  • #1
eohjelle
3
0
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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  • #2
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
 
  • #3
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.
 
  • #4
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 :)
 
  • #5
@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?
 
  • #6
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.
 

1. What is impulse?

Impulse is the change in momentum of an object, which is equal to the force applied to the object multiplied by the time interval over which the force acts.

2. How does impulse relate to energy?

Impulse is directly related to the change in kinetic energy of an object. This is because impulse is equal to the force applied multiplied by the distance over which the force acts, which is the work done on the object. This work results in a change in kinetic energy.

3. What is the net force?

The net force is the sum of all forces acting on an object. It takes into account both the magnitude and direction of each force.

4. Why is the net force important when discussing impulse and energy?

The net force is important because it determines the amount of work done on an object, which ultimately affects the object's change in kinetic energy. When the net force is zero, no work is being done on the object and therefore there is no change in kinetic energy.

5. How does the net force being zero affect an object's impulse and energy?

When the net force is zero, the impulse on the object is also zero. This means that there is no change in the object's momentum or kinetic energy. This is because no work is being done on the object, so there is no transfer of energy. Essentially, the object remains in a state of equilibrium.

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