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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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Most popular questions from this chapter

The forces on a small airplane (mass \(1160 \mathrm{kg}\) ) in horizontal flight heading eastward are as follows: gravity \(=16.000 \mathrm{kN}\) downward, lift \(=16.000 \mathrm{kN}\) upward, thrust \(=1.800 \mathrm{kN}\) eastward, and \(\mathrm{drag}=1.400 \mathrm{kN}\) westward. At \(t=0,\) the plane's speed is \(60.0 \mathrm{m} / \mathrm{s} .\) If the forces remain constant, how far does the plane travel in the next \(60.0 \mathrm{s} ?\)
A bike is hanging from a hook in a garage. Consider the following forces: (a) the force of the Earth pulling down on the bike, (b) the force of the bike pulling up on the Earth, (c) the force of the hook pulling up on the bike, and (d) the force of the hook pulling down on the ceiling. Which two forces are equal and opposite because of Newton's third law? Which two forces are equal and opposite because of Newton's first law?
A horse is trotting along pulling a sleigh through the snow. To move the sleigh, of mass \(m,\) straight ahead at a constant speed, the horse must pull with a force of magnitude \(T.\) (a) What is the net force acting on the sleigh? (b) What is the coefficient of kinetic friction between the sleigh and the snow?
A 6.0 -kg block, starting from rest, slides down a frictionless incline of length \(2.0 \mathrm{m} .\) When it arrives at the bottom of the incline, its speed is \(v_{\mathrm{f}} .\) At what distance from the top of the incline is the speed of the block \(0.50 v_{\mathrm{f}} ?\)
A hanging potted plant is suspended by a cord from a hook in the ceiling. Draw an FBD for each of these: (a) the system consisting of plant, soil, and pot; (b) the cord; (c) the hook; (d) the system consisting of plant, soil, pot, cord, and hook. Label each force arrow using subscripts (for example, \(\overrightarrow{\mathbf{F}}_{\mathrm{ch}}\) would represent the force exerted on the cord by the hook).
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