Cool (finally!)

A 1 lb point mass is held up by two ideal ropes. One rope is vertical and 55 cm long. The other is at an angle from the vertical rope. It is attached to the same "ceiling" as the other rope, so it looks something like this:

Code: Select all

```
---------------------
| /
| /
| /
|/
O
```

Imagine you suddenly decrease the length of the rope to the right by half of the length of the rope to the left. Find the tension in each rope (magnitude and direction) after the system reaches static equilibrium if the angle between them was originally

a) as close to 0 degrees as possible

b) 30 degrees

c) 45 degrees

d) 60 degrees

e) as close to 90 degrees as possible

EDIT: Unfortunately, I made an error when I first did this problem, and the algebra is more complicated than I thought (meaning very time-consuming). Thus, I will ask another problem :/

Three masses are held up to a ceiling by three ropes, like so:

The ball on top has a mass of 5 kg, the ball in the middle 3 kg, the ball on the bottom 1 kg. Assuming the ropes are ideal, find the tension in each rope.