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

eohjelle

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?

Woopydalan

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

DaleSpam

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.

afreiden

It goes partly into deforming the wall

Everything moves :)

eohjelle

@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?

DaleSpam

Yes, almost always.