# Where is the mistake in this reasoning?

#### Cobain

Situation #1.
In space, an object is moving with a constant velocity in an inertial reference frame. The object is connected to a winch (winch “A”) with a rope. Winch “A” is resting in the inertial reference frame. The rope’s end that is on the object’s side is not simply tied to it. It is connected to another winch (winch “B”) on the object. Winch “B” winds the rope in a way that it keeps the rope streached, but it doesn’t draw it (ie. the winch’s action doesn’t affect the object’s velocity).
Then, winch “A” starts winding the rope’s other end. After working for some time it stops. As it worked, it consumed some amount of energy. That energy is transfered to the object.

Situation #2.

Evereything is as in the situation #1 except these two:

1. The object is moving faster;
2. Winch “B” winds the rope correspondingly faster to keep it streached.

In both the situation the energies that are used to power winches “A” are same and they are transferred to the objects (ie. the objects gained same energies).

But in the situation #2 the object travells longer distance in the period the winch “A” works (because it was moving faster) . Hence the work done by the force that draws the object to winch “A” is greater. That means, in situation 2, the object gains more energy than in situation 1.

#### benit13

Situation #1.
The rope’s end that is on the object’s side is not simply tied to it. It is connected to another winch (winch “B”) on the object. Winch “B” winds the rope in a way that it keeps the rope streached, but it doesn’t draw it (ie. the winch’s action doesn’t affect the object’s velocity).
?

Can you please draw a diagram?

#### Woody

I can't work out the purpose of winch 2.

By setting the scenario "in space" I am guessing that you are implying it is in "free-fall" (without gravity).

#### Cobain

The purpose of the winch B is to ensure when winch A starts to pull the rope, it pull equally streached ropes in both scenarios.

The object is in zero-gravity space.

#### oz93666

The puzzle has not been fully defined ...

the mass of winch A has not been given .(it must have a mass otherwise it cannot 'pull')

the combined mass of the object and winch B has not been given .

basically you have two masses connected by a rope , the system does not know or care which winch creates the pull.

As soon as either winch makes the slightest pull the two masses have a relative velocity which draws them together.

#### Woody

I have been trying to understand your word picture.

Winch A starts pulling the object,
The object accelerates until it is moving at the same rate as the rate at which the winch is pulling.
Note the above scenario already assumes that:
Either the winch is pulling at a varying rate from zero up to some maximum
Or the rope is stretching to allow the object to accelerate (or a bit of both)
The object can't go from zero to full speed without accelerating.

The rope will remain taut throughout the above process.

Now Winch A stops, but the object keeps moving (assuming negligible friction)
The rope will go slack.
Is this where Winch B starts taking up the slack?

Note (Oz) that I have assumed that Winch A is attached to a structure
which is sufficiently more massive than the object and rope etc.
that its motion (relative to the motion of the object) can be assumed negligible.
(but not so massive that its gravitational attraction becomes significant).

#### Woody

I've looked again at your original post;

You do say that the object is initially moving,
the winches, it seems, are just taking up the slack.

In this scenario the winches are actually doing nothing at all!

All the winches will be doing is replacing any losses (friction) in the system.