Question #ab711

1 Answer
Apr 30, 2016

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!)