(Solved): 5. Volcanologists need a lava sample from an active lava pool below a plateau inside the volcano. A ...

5. Volcanologists need a lava sample from an active lava pool below a plateau inside the volcano. After one end of a rope is anchored to the rock, another scientist hikes around the plateau rim so that the rope and an attached cable hang over the lava pool. The cable is dipped into the lava pool and the lava that congeals on the cable is retrieved. (This was done at Nyiragongo in Africa). When the cable with the lava sample has a weight of $125\mathrm{N}$, how large is the tension in the rope? (Hint: make your force diagram for the junction between the cable and the rope and don't worry about the fact that the rope has mass too) The actual apparatus has a pulley in the middle of the rope. The cable parallels one side of the rope, goes over the pulley and down to the lava pool. The reason for this is that pimply tightening the rope can't lift the lava sample out. Here's why: calculate how much tension would be needed in the rope to decrease the angle to $5^{?}$.