Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 16

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?

Short Answer

Expert verified
Answer: The force required is approximately 2.943 N.

Step by step solution

01

Identify the given values

The given values are: - Depth of the leak below the water surface: \(h = 3.0\,\mathrm{m}\) - Area of the hole in the dike: \(A = 1.0\,\mathrm{cm}^2\) The density of water is approximately \(\rho = 1000\,\mathrm{kg/m^3}\) and the acceleration due to gravity is \(g = 9.81\,\mathrm{m/s^2}\).
02

Convert the area to SI units

Since we are dealing with SI units (meters and kilograms), we need to convert the area of the hole from square centimeters to square meters. \(1\,\mathrm{cm}^2\) = \(0.0001\,\mathrm{m}^2\) Therefore, the area of the hole in the dike is: \(A = 0.0001\,\mathrm{m}^2\)
03

Calculate the pressure exerted by the water

We are now ready to calculate the pressure exerted by the water at a depth of 3 meters. We'll use the formula \(P = h \rho g\), where \(h = 3.0\,\mathrm{m}, \rho = 1000\,\mathrm{kg/m^3}\), and \(g = 9.81\,\mathrm{m/s^2}\) \(P = (3.0\,\mathrm{m})(1000\,\mathrm{kg/m^3})(9.81\,\mathrm{m/s^2}) = 29,430\,\mathrm{Pa}\)
04

Calculate the force required to stop the leak

Finally, we can now calculate the force required to stop the leak using the formula \(F = PA\), where \(P = 29,430\,\mathrm{Pa}\) and \(A = 0.0001\,\mathrm{m}^2\) \(F = (29,430\,\mathrm{Pa})(0.0001\,\mathrm{m}^2) = 2.943\,\mathrm{N}\) The force that the Dutch boy must exert to save the town is approximately \(2.943\,\mathrm{N}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The body of a 90.0 -kg person contains \(0.020 \mathrm{m}^{3}\) of body fat. If the density of fat is \(890 \mathrm{kg} / \mathrm{m}^{3},\) what percentage of the person's body weight is composed of fat?
(a) When ice floats in water at \(0^{\circ} \mathrm{C},\) what percent of its volume is submerged? (b) What is the specific gravity of ice?
A manometer using oil (density \(0.90 \mathrm{g} / \mathrm{cm}^{3}\) ) as a fluid is connected to an air tank. Suddenly the pressure in the tank increases by \(0.74 \mathrm{cm}\) Hg. (a) By how much does the fluid level rise in the side of the manometer that is open to the atmosphere? (b) What would your answer be if the manometer used mercury instead?
You are hiking through a lush forest with some of your friends when you come to a large river that seems impossible to cross. However, one of your friends notices an old metal barrel sitting on the shore. The barrel is shaped like a cylinder and is \(1.20 \mathrm{m}\) high and \(0.76 \mathrm{m}\) in diameter. One of the circular ends of the barrel is open and the barrel is empty. When you put the barrel in the water with the open end facing up, you find that the barrel floats with \(33 \%\) of it under water. You decide that you can use the barrel as a boat to cross the river, as long as you leave about $30 \mathrm{cm}$ sticking above the water. How much extra mass can you put in this barrel to use it as a boat?
Near sea level, how high a hill must you ascend for the reading of a barometer you are carrying to drop by 1.0 cm Hg? Assume the temperature remains at \(20^{\circ} \mathrm{C}\) as you climb. The reading of a barometer on an average day at sea level is $76.0 \mathrm{cm}$ Hg. (W) tutorial: gauge)
See all solutions

Recommended explanations on Physics Textbooks

Electrostatics

Read Explanation

Thermodynamics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Torque and Rotational Motion

Read Explanation

Linear Momentum

Read Explanation

Translational Dynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free