# Does a box of Pendulum's weigh more if they are swinging?

The question is more specifically to explain why the box doesn't weigh more, because if it did then I could revolutionize space travel.

Consider a rigid box suspending two counter oscillating pendulums of mass m/2. Starting against the top, at the bottom of their swing the masses will be moving with a speed of $$\sqrt{2gl}$$ where $$l$$ is the length of the pendulum. The sum tension in the lines at this moment should be equal to the weight of the masses plus the centrifugal force: $$T = mg + \frac{mv^2}{r}$$. Plugging in the speed at the bottom gives a tension of $$T = 3mg$$. I figure the weight of the full box is the weight of the box material plus the downward component of the tension, as any horizontal components are canceled by the counter-oscillating setup.

So it seems at the bottom of the pendulums swing, the box weighs more than when with stationary pendulums. And, intuitively, the box will weigh less as the tension goes to zero at the apex.

I can envision a box suspending two sets (four total) of counter rotating powered rods that are out of phase such that at any moment there is a non-zero downward component of tension, making this box always heavier when the rods are moving.

Why couldn't I use this "extra weight" to transfer momentum?

• you probably could. What 's wrong with that? How will you make the pendulums swing in space? Commented Mar 1, 2023 at 18:20
• The same centrifugal forces would be generated if the pendulums were motorized rods, this is the case I describe in the second to last paragraph. I'm sure the reaction forces on the box must have something to do with it, but I can't resolve how. Commented Mar 1, 2023 at 18:29
• Why do you need counter-rotating pendulums to generate an oscillating force on the box? Why not just one heavy ball bouncing up and down on a spring? Commented Mar 2, 2023 at 13:00
• That is a very good point. I already understand where my reasoning failed, but this example highlights it well. Commented Mar 2, 2023 at 13:01