Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 476

If the water falls from a dam into a turbine wheel \(19.6 \mathrm{~m}\) below, then the velocity of water at the turbine is \(\ldots \ldots\) \(\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(9.8 \mathrm{~m} / \mathrm{s}\) (B) \(19.6 \mathrm{~m} / \mathrm{s}\) (C) \(39.2 \mathrm{~m} / \mathrm{s}\) (D) \(98.0 \mathrm{~m} / \mathrm{s}\)

Short Answer

Expert verified
The velocity of the water at the turbine is approximately \(19.6\) m/s. The correct answer is (B).

Step by step solution

01

Identify the variables

Here, we need to identify the known and unknown variables in the problem. The known variables are the height of the falling water (h) which is 19.6 m, and the acceleration due to gravity (g) which is 9.8 m/s². The unknown variable is the final velocity of water at the turbine (v).
02

Choose the appropriate kinematic equation

Since we are given height and acceleration, and need to find final velocity, we can choose the equation: \(v^2 = u^2 + 2gh\), where u is the initial velocity (0 m/s as the water starts at rest), g is the acceleration due to gravity, and h is the height of the water.
03

Plug in the values

Now, we will substitute the given values into the equation: \(v^2 = 0^2 + 2 (9.8) (19.6)\).
04

Calculate the velocity

By calculating the values, we end up with the equation: \(v^2 = 2 (9.8) (19.6)\), and therefore: \(v^2 = 384.16\). Next, take the square root of both sides to find the final velocity (v): \[v = \sqrt{384.16}\]. Finally, we get the velocity of the water at the turbine: \(v ≈ 19.6\) m/s. Among the given options, (B) is closest to our calculated value: 19.6 m/s.

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

A billiard ball moving with a speed of \(8 \mathrm{~m} / \mathrm{s}\) collides with an identical ball originally at rest. If the first ball stops after collision, then the second ball will move forward with a speed of .... (elastic collision) (A) \(8 \mathrm{~m} / \mathrm{s}\) (B) \(4 \mathrm{~m} / \mathrm{s}\) (C) \(16 \mathrm{~m} / \mathrm{s}\) (D) \(1.0 \mathrm{~m} / \mathrm{s}\)

The mass of a car is \(1000 \mathrm{~kg}\). How much work is required to be done on it to make it move with a speed of \(36 \mathrm{~km} / \mathrm{h}\) ? (A) \(2.5 \times 10^{4} \mathrm{~J}\) (B) \(5 \times 10^{3} \mathrm{~J}\) (C) \(500 \mathrm{~J}\) (D) \(5 \times 10^{4} \mathrm{~J}\)

A sphere of mass \(\mathrm{m}\) moving the velocity \(\mathrm{v}\) enters a hanging bag of sand and stops. If the mass of the bag is \(\mathrm{M}\) and it is raised by height \(\mathrm{h}\), then the velocity of the sphere was (A) \([\\{\mathrm{m}+\mathrm{M}\\} / \mathrm{m}] \sqrt{(2 \mathrm{gh})}\) (B) \((\mathrm{M} / \mathrm{m}) \sqrt{(} 2 \mathrm{gh})\) (C) \([\mathrm{m} /\\{\mathrm{M}+\mathrm{m}\\}] \sqrt{(2 \mathrm{gh})}\) (D) \((\mathrm{m} / \mathrm{M}) \sqrt{(2 \mathrm{gh})}\)

The bob of simple pendulum (mass \(\mathrm{m}\) and length 1 ) dropped from a horizontal position strike a block of the same mass elastically placed on a horizontal frictionless table. The K.E. of the block will be (A) \(2 \mathrm{mg} 1\) (B) \(\mathrm{mg} 1 / 2\) (C) \(\mathrm{mg} 1\) (D) zero

A mass of \(\mathrm{M} \mathrm{kg}\) is suspended by a weight-less string, the horizontal force that is required to displace it until the string makes an angle of \(60^{\circ}\) with the initial vertical direction is (A) \(\mathrm{Mg} / \sqrt{3}\) (B) \(\mathrm{Mg} \cdot \sqrt{2}\) (C) \(\mathrm{Mg} / \sqrt{2}\) (D) \(\mathrm{Mg} \cdot \sqrt{3}\)
See all solutions

Recommended explanations on English Textbooks

Morphology

Read Explanation

Prosody

Read Explanation

English Grammar

Read Explanation

History of English Language

Read Explanation

Creative Story

Read Explanation

Pragmatics

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