Question

Question #ab711

Answer 1

A mass at least =340kg

Explanation:

I think, looking at the picture, that the question is what mass has to be placed over the `3m^2` hole to move the boulder sitting over the `9m^2` hole.

The question is based on Pascal's principle that states that pressure in a liquid is transmitted equally in all directions. We will need to assume that the lava behaves like a liquid.

Pressure is given by force divided by area, or `P=F/A`

The boulder has a weight of 10,000N. hence a force exceeding this will need to be transmitted by the pressure in the fluid to move it.
The boulder is sitting on area of `9m^2`. Hence pressure will need to be greater than:
`P=F/A=10000/9`

If a weight, `mg` is placed over the `3m^2` hole, then the force
exerted on the fluid below will be:
`P=F/A=(mg)/3`

We need this pressure, which will be transmitted through the lava, to move the boulder so:
`(mg)/3>10000/9`
which simplifies to:
`m>10000/(g*3)`
If we take `g=9.81ms^-2` then
`m>339.8 kg`

So they should put a mass of at least 340kg to enable them to push it off (provided they don't get fried by the molten lava first!)