Question

A person with a mass of 76 kg and a volume of 0.094 m3 floats quietly in water.What is the volume of the person that is above water?If an upward force F is applied to the person by a friend, the volume of the person above water increases by 0.0015 m3 . Find the force F.

Answer 1

Given data:

M = 76 kg

V = 0.094 m³

v_b = 0.0015 m³

(a)

F_g = m*g

F_g = 76*9.81

F_g = 745.56 N

The buoyancy force is acting upward

F_b = (volume of the person below the water)*(weight of water)

F_b = (total volume - volume above water)*(weight of water)

F_b = (0.094 m³ - v_a)*(1000 kg/m³* 9.81)

F_b = 922.14 – 9810*v_a

F_b = F_g

922.14 – 9810*v_a = 745.56

v_a = 0.018 m³

(b)

F_g = F_b + F_Friend

745.56 = (V – (v_a+v_b))*(1000kg/m³*9.81) + F_Friend

745.56 = [0.094 - (0.018 + 0.0015)]*(1000 kg/m³* 9.81) + F_Friend

745.56 – 730.845 = F_Friend

Friend = 14.7 N