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Chapter 4: Problem 20

A man is lazily floating on an air mattress in a swimming pool. If the weight of the man and air mattress together is \(806 \mathrm{N},\) what is the upward force of the water acting on the mattress?

Short Answer

Expert verified
Answer: The upward force of the water acting on the man and the air mattress is 806 N.

Step by step solution

01

Identify the forces acting on the system

In this problem, we have two forces acting on the man and the air mattress: the downward force due to the weight of the system (gravity) and the upward force due to the water (buoyancy).
02

Apply the concept of equilibrium

Since the man and the air mattress are lazily floating, it means they are in equilibrium. In equilibrium, the downward force (weight) is equal to the upward force (buoyancy), so we can write this as: \(F_{upward} = F_{downward}\)
03

Use the given weight to determine the upward force

We know the downward force is the weight of the man and the air mattress, which is 806 N. Now we can equate it to the upward force to find its value: \(F_{upward} = F_{downward} = 806 \mathrm{N}\) Thus, the upward force of the water acting on the mattress and man is 806 N.

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