Explanation:
Draw a free body diagram. Ā There are three forces on the block:
Weight force mg pulling down,
Buoyancy force B pushing up,
Tension force T pushing up.
Sum of the forces in the y direction:
āF = ma
B + T ā mg = 0
T = mg ā B
Buoyancy is the weight of the displaced fluid:
T = mg ā ĻVg
The block is fully submerged, so the volume of displaced fluid equals the volume of the block. Ā The volume of the block is its mass divided by its density.
T = mg ā Ļ (m/Ļā) g
T = mg (1 ā Ļ/Ļā)
Plug in values and solve.
T = (0.5 kg) (10 m/sĀ²) (1 ā (1000 kg/mĀ³) / (8000 kg/mĀ³))
T = (5 N) (1 ā ā )
T = 4.375 N
