A beaker of mass 5kg containing oil of mass 17.4 kg and density 8.5 x102kg/m3 rests on the scale
A block of iron of mass 6.7kg is suspended from the spring scale and completely submerged in the oil as shown in Figure below. Determine the equilibrium readings of lower scale in newtons. ( iron density is 7200 kg/m3).
ok, the first thing to do is figure the bouyant force on the iron.
forceB=density*volume*g
= volume iron*density oil*g
= massiron/density iron * density oil*g
so the upper sting is holding the weight of iron, less bouyant force or
upper=6.7*g-forceB
and the lower force is the weight of the beaker, oil, and bouyant force on the iron.
lowerforce=5*g + 17.4*g + force B
were g= 9.8N/kg
To determine the equilibrium reading of the lower scale in newtons, we need to consider the buoyant force acting on the block of iron when it is submerged in the oil.
The buoyant force is equal to the weight of the liquid displaced by the object. In this case, the block of iron displaces the oil. The weight of the displaced oil is given by the formula:
Weight of displaced oil = volume of oil x density of oil x acceleration due to gravity
First, let's calculate the volume of the oil displaced by the block of iron. The volume of an object submerged in a fluid can be calculated using Archimedes' principle:
Volume of displaced oil = volume of block of iron
The volume of the block of iron is given by its mass divided by its density:
Volume of block of iron = mass of block of iron / density of block of iron
Now, we can calculate the weight of the displaced oil:
Weight of displaced oil = volume of oil x density of oil x acceleration due to gravity
Next, we need to calculate the total weight acting on the lower scale. This includes the weight of the beaker and the weight of the oil:
Weight on lower scale = weight of beaker + weight of oil
The weight of the beaker is given by the mass of the beaker multiplied by the acceleration due to gravity:
Weight of beaker = mass of beaker x acceleration due to gravity
Finally, the equilibrium reading of the lower scale in newtons is equal to the weight on the lower scale minus the weight of the displaced oil:
Equilibrium reading of lower scale = weight on lower scale - weight of displaced oil
By following these steps and plugging in the given values, you can find the equilibrium reading of the lower scale in newtons.