# Effect of internal forces on the weight of a body.

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1. Jan 31, 2016

### physicsmaths1613

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A man is holding a closed cage on the palm of his hand with a bird in it.
When the bird flies with an upward acceleration inside the cage, it feels heavier.
But the force due to the bird in the cage is actually an internal force on the cage, and internal forces don't cause acceleration of the body, then how does the cage feel heavier?

2. Jan 31, 2016

### ZapperZ

Staff Emeritus
Newton's 3rd Law.

The bird's wings are pushing on the air to keep it afloat, so there is a downward force exerted by the bird onto the air, which then transfers to the downward force onto the bottom of the cage.

If you stand on a weighing scale, look at the reading on the scale as you toss a ball up into the air. Same principle here.

Zz,.

3. Jan 31, 2016

### physicsmaths1613

But the weight machine is not a closed system like the cage. Please point out the flaws in my logic.If we are in a closed box no matter how much force we apply, we can't accelerate it. Similarly, if the bird is in the closed cage, no matter what force it applies(through the air) the cage won't accelerate, thus there won't be any change of weight.

4. Jan 31, 2016

### CWatters

Why do you consider the cage to be a closed system? Would adding some wire hoops make the weighing machine a closed system?

5. Jan 31, 2016

### physicsmaths1613

In that case the system is only the weighing machine. Here we have the bird in the system already. We want to see how its motion affects the weight of cage. In case of weighing machine we weren't already standing on the machine.

6. Jan 31, 2016

### ZapperZ

Staff Emeritus
Look at the scenario you gave! You stated that ".... When the bird flies with an upward acceleration inside the cage.... ". Whether you agree with it or not, the bird is accelerating upwards, which means that there is a net force pushing it up (due to the air). And thus, the air pushes down on the bottom of the cage.

The fact that it is "air" and not a rigid substance, in this case, does not matter. You might as well replace air with a rigid perch attached to the bottom of the cage, and have the bird jump upwards from it.

Zz.

7. Jan 31, 2016

### Staff: Mentor

I agree with ZZ. But, if air cannot enter of leave the cage and the bird is just hovering (rather than accelerating) at steady state, then there is no net acceleration for the center of mass for the combination of air, bird, and cage, and the upward force required to keep the system stationary is just the weight of the air, bird, and cage.

Chet

8. Jan 31, 2016

### nasu

No net acceleration of CM does not mean that the parts of the system cannot accelerate. The OP starts with a flawed assumption.
"If we are in a closed box no matter how much force we apply, we can't accelerate it" is simply not true.
If we accelerate in the opposite direction we can do this. Like running in a boat from end to the other, for example. The fact that it is "closed" is irrelevant.

You can be in a closed box on a scale. If you jump up, the force on the scale will change. If the box is not on the scale but somehow floating freely in space, it will accelerate as there is no opposite force from the scale or other support.

9. Feb 1, 2016

### ehild

Internal forces don't cause acceleration of the centre of mass.
The cage and the bird inside make a system, but it is not closed as the man holds it on his hand. The hand exerts force on the cage. That means an external force on the system. The other force is gravity, and the force of the palm and gravity balance each other till the bird is in rest in the cage.
When the bird accelerates upwards the cage stays on the palm of the man. The birds moves higher, so the centre of mass also moves higher, has an upward acceleration. The accelerating CM means extra upward force, exerted by the palm. That is why the system feels heavier.
In case the cage was isolated (in free space) and the bird accelerated in one direction, the cage would accelerate in the opposite direction so as the CM did not accelerate.