Question

a rectangular block of density 50g/cm³ measuring 8cm by 4cm by 2.5cm is attached to a spring balance. The block is lowered into a beaker of mass 100g with 500cm³ of water and placed on a weight measuring balance. calculate the readings on the spring balance and and the weight balance in newtons when in air and when the block is totally submerged in water.

Answer 1

The weight of block in air (readings on the spring balance when in air):

$$W=mg=\rho V·g=\\ =(0.001·50)(8·4·2.5)·9.8=39.2\text{ N}.$$

The weight of block in water (readings on the spring balance when in water):

$$W=mg-\rho_w gV=\\ =39.2-1000·9.8·(0.08·0.04·0.025)=38.42\text{ N}.$$

The weight of beaker with the block submerged in water (readings on the weight balance):

$$W=mg+m_bg+m_wg=g(m+m_b+m_w)=\\ =g(\rho V+m_b+\rho_wV_w)=45.1\text{ N}.$$