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Chapter 9: Problem 7

A container is filled with gas at a pressure of $4.0 \times 10^{5} \mathrm{Pa}\( The container is a cube, \)0.10 \mathrm{m}$ on a side, with one side facing south. What is the magnitude and direction of the force on the south side of the container due to the gas inside?

Short Answer

Expert verified
Answer: The magnitude of the force is 4000 N, and the direction is towards the north.

Step by step solution

01

Calculate the area of the south side of the container

The container is a cube, with each side measuring \(0.10 \ \text{m}\). Therefore, the area of the south side of the container can be calculated by squaring its length: \(A = (0.10 \ \text{m})^2 = 0.01 \ \text{m}^2\)
02

Use the pressure and area to calculate the force

Recall that the formula for pressure is \(P = \frac{F}{A}\). Rearrange this formula to solve for force: \(F = P \times A\). Using the given pressure of \(4.0 \times 10^{5} \ \text{Pa}\) and the calculated area of the south side, the force on the south side is: \(F = (4.0 \times 10^{5} \ \text{Pa})(0.01 \ \text{m}^2) = 4000 \ \text{N}\)
03

Determine the direction of the force

The force will be exerted by the gas inside the container, as it pushes against the south side. As a result, the force will act in the opposite direction (north) since the gas is exerting pressure on the inside of the south side.
04

Present final answer

The magnitude of the force on the south side of the container due to the gas inside is 4000 N, and the direction of the force is towards the north.

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Most popular questions from this chapter

A lid is put on a box that is \(15 \mathrm{cm}\) long, \(13 \mathrm{cm}\) wide, and \(8.0 \mathrm{cm}\) tall and the box is then evacuated until its inner pressure is \(0.80 \times 10^{5} \mathrm{Pa} .\) How much force is required to lift the lid (a) at sea level; (b) in Denver, on a day when the atmospheric pressure is \(67.5 \mathrm{kPa}\) ( \(\frac{2}{3}\) the value at sea level)?
In the Netherlands, a dike holds back the sea from a town below sea level. The dike springs a leak \(3.0 \mathrm{m}\) below the water surface. If the area of the hole in the dike is \(1.0 \mathrm{cm}^{2},\) what force must the Dutch boy exert to save the town?
A woman's systolic blood pressure when resting is \(160 \mathrm{mm}\) Hg. What is this pressure in (a) \(\mathrm{Pa},\) (b) \(\mathrm{lb} / \mathrm{in}^{2}\) (c) atm, (d) torr?
A sphere of radius \(1.0 \mathrm{cm}\) is dropped into a glass cylinder filled with a viscous liquid. The mass of the sphere is \(12.0 \mathrm{g}\) and the density of the liquid is \(1200 \mathrm{kg} / \mathrm{m}^{3} .\) The sphere reaches a terminal speed of \(0.15 \mathrm{m} / \mathrm{s} .\) What is the viscosity of the liquid?
An IV is connected to a patient's vein. The blood pressure in the vein has a gauge pressure of \(12 \mathrm{mm}\) Hg. At least how far above the vein must the IV bag be hung in order for fluid to flow into the vein? Assume the fluid in the IV has the same density as blood.
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