Answer:
2870 N
Explanation:
There are three forces on the mattress. Weight of the mattress, weight of the person, and buoyancy.
∑F = ma
B - mg - Mg = 0
Buoyancy is equal to the weight of the displaced fluid.
ρVg - mg - Mg = 0
ρV - m = M
Plugging in values:
M = (1000 kg/m³) (0.75 m × 2.25 m × 0.175 m) - 2 kg
M = 293 kg
The person's weight is therefore:
Mg = 293 kg × 9.8 m/s²
Mg = 2870 N
