Do Vessels with the Same Base Area Have Different Weighing Scale Readings?

[Abhishekdas]

Reading on a weighing scale...

Homework Statement

Two vessels have the same base area but different shapes.The first vessel takes twice the volume of water that the second vessel requires to fill up to a particular common height. IS the force excerted by water on the base of the vessel same in the two cases? If so, why do the vessels filled with water to the same height have different redings on a weighing scale...

Homework Equations

P=P₀ + h*density*g

The Attempt at a Solution

Now i got the first part that the force excerted by water on the base of the vessel in both cases is same...because h,density of water and g is smae in both cases...

And the second part is obvious but what is the machanism of a weighing scale...I thought the weighing scale measures normal reaction...So in this case isn't the normal reaction same s the force excerted ny water in the base? The extra weight is balanced by the walls...SO the normal reaction is apparently same...So how is the reading dfferent...From one angle this question seems dumb coz its like saying when i stand on a scale the muscles balance the weight of arms and stuff so the weing scale should give the weight of only the part vertically above my feet...But still...I would like to get an answer for this question...Actually don't know why we write normal reaction = mg...when certain parts of a body are not in contact with the ground or scale...
If some one asks me why is Normal reaction = mg...I will say that body is in equillibrium and hence external force shud add up to zero...
But personally i am not convinced...

 

[supratim1]

force exerted is not same.
its PRESSURE, force exerted per unit AREA that is same.

 

[Abhishekdas]

At that point if pressure is same force (P*A) is same...

 

[supratim1]

that is at base. the remaining force will be exerted on the lateral surface of the container, which must have a y component.

 

[amy andrews]

Isn't the force exerted on the base different in the two containers? Because one has a larger volume, that means that it has a larger mass of water in (and therefore weight exerted on) it-doesn't this mean that the force exerted on the base of one is larger than that exerted on the base of another? I'm probably very wrong...

 

[supratim1]

hello amy...

thats what i said. pressure at base is same for both. since base area is same, so total force on base is same. but NET force downwards is more for the one with more water, the remaining force being the y components of forces at the sides of the container (which can never be right cylindrical, if the first one is right cylindrical).

 

[Abhishekdas]

I know...that the downward force is same...But doesn't the weighing scale measure only normal reaction...and why is normal reaction different from force at the base...? Force at base is same for both but normal reaction isnt...