Hydrostatic Force and Calculus Concepts

Hydrostatic Force and Calculus Concepts

Assessment

Interactive Video

Mathematics, Physics, Science

10th - 12th Grade

Practice Problem

Hard

Created by

Aiden Montgomery

FREE Resource

The video tutorial explains how to calculate the hydrostatic force exerted on a dam by water pressure. It begins with an overview of the dam's structure and water level, followed by an explanation of hydrostatic force and pressure. The tutorial then sets up the integral needed for force calculation, detailing the calculation of weight density and distance below the water surface. It also derives the width of the dam as a function of Y. Finally, the video demonstrates the total force calculation using the integral, providing a step-by-step approach to solving the problem.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the shape of the dam wall facing the water?

A circle

A rectangle

A region above the curve y = 0.5x^4

A triangle

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the water level below the top of the dam?

160 meters

130 meters

100 meters

30 meters

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which formula is used to calculate hydrostatic force?

P = F/A

F = ma

Integral of w * D(y) * L(y)

E = mc^2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does 'D(y)' represent in the integral?

Height of the dam

Density of water

Distance below the surface

Width of the dam

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is calculus used in calculating hydrostatic force?

To account for changing pressure with depth

To simplify the problem

To find the area of the dam

To measure the water density

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the weight density of water used in the example?

9,800 N/m^3

9.8 m/s^2

1,000 kg/m^3

62.4 lb/ft^3

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the width of the dam, L(y), expressed as a function of y?

L(y) = 130 - y

L(y) = 2x

y = 0.5x^4

2 * the 4th root of 2y

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