Question

A 34-cm-tall, 6.0-cm-diameter cylindrical beaker is filled to its brim with water.What is the downward force of the water on the bottom of the beaker?

Answer 1

h = height of the beaker = 34 cm = 0.34 m

ρ = density of water in the beaker = 1000 kg/m³

g = acceleration due to gravity = 9.8 m/s²

P₀ = atmospheric pressure = 101325 pa

P = pressure at the bottom of the beaker

Pressure at the bottom of the beaker is given as

P = P₀ + ρ g h

inserting the values

P = 101325 + (1000) (9.8) (0.34)

P = 104657 Pa

d = diameter of cylindrical beaker = 6 cm = 0.06 m

A = area of the bottom of the beaker = (0.25)πd² = (0.25) (3.14) (0.06)² = 0.00283 m²

Downward force of the water on the bottom of the beaker is given as

F = PA

F = (104657) (0.00283)

F = 296.2 N