# Path of a block suspended by two parallel cords

1. Nov 8, 2013

### stroustroup

I have an argument with classmates about the trajectory that the block will have (circle, ellipse, something else...).

The configuration is similar to this image.
http://minireference.com/_media/physics/momentum-bullet-speed-block.jpg?w=400

Initially, the block will move horizontally, after which it will move up as well, since the strings have constant length.

But will the path be a circle, an ellipse, or another shape?

I believe it will be a circle because the ropes will always be parallel and the middle axis of the parallelogram formed by these two ropes will also have constant length. So the distance of the middle point on top of the block to the ceiling is constant, which means it's a circle.

They believe it should be an ellipse, because the strings might not be always taut.
Which is true?

2. Nov 8, 2013

### elegysix

The key is whether the strings are always taut.
I imagine this will rock like a pendulum, but I think you'll have to break out the calculus if you want a more detailed solution.
Or just build one and give it a push. Shouldn't be too hard to make.

3. Nov 8, 2013

### stroustroup

Well, in this particular case when the bullet hits the block horizontally, the initial moment of the system about the center of mass is 0 since the bullet moves towards the block's center. The angular impulse is 0, since there are no net torque. So after the collision, the angular momentum must be the same as initially (i.e. 0) and so the block should always remain horizontal. In that case the strings will always be taut, I think.

But in our case, the bullet hits the block differently. The point of impact is the midpoint between the two cords, and the angle is 20 deg. to the horizontal. Not sure about the angular impulse now. The block might also spin around itself while swinging?