Sorry this might seem like a dumb question, but I'm having trouble understanding the concept behind buoyant force and scale readings.
Suppose I have a beaker filled with water, and the beaker is placed on a measuring scale.
a) If I then place a ball into the beaker, the ball floats, what will be scale reading be? I understand that Mg=Buoyant force, since the ball floats, they cancel out. Does that mean there's no change in scale reading?
b) If I place a ball and the ball submerges completely under the water, but does not touch the base of the beaker, what will the scale reading be? Now that Mg>Buoyant force, does the scale reading increase by the difference of the two? Mg-Buoyant force?
c) If I place a ball and the ball completely sinks under the water and touches the base of the beaker, what will be scale reading be? I understand that Mg>>>Fb, but why does Fb play no effect in the scale reading in this case?
Best Answer
Buoyant force has no effect on the interaction between the beaker and the scales it stands on.
The scales will register a weight which is the sum of the weights of the beaker, water and ball.
Consider that if the ball is at least partially immersed so that some part is below the level of water, it has displaced some water and so raised the level of the water in the beaker.
The water pressure at the bottom is a function of the height of the water column above it and so is a higher pressure. Since pressure acts normally to the interface between water and beaker base it presses down on the base of the beaker which transmits this force to the scales.