Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Water falls without splashing at a rate of 0.250 L/s from a height of 2.60 m into a bucket on a scale. If the bucket is originally empty, what does the scale read in Newton’s 3.00 s after water starts to accumulate in it?

The scale read in Newton’s 3.00 s after water starts to accumulate in it is 16.5 N.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Concept

The kinetic energy to particle is:

$K = \frac{1}{2} {mv}^{2}$

The potential energy to particle is:

U = mgy

Step 2: Reading of scale

After 3.00 s of pouring, the bucket contains $(3.00 s) (0.250 L/s) = 0.750 L$ of water with mass, $(0.750 L) (1 kg / 1 L) = 0.750 kg$ and feeling gravitational force $(0.750 kg) (9.80 m / s^{2}) = 7.35 N$ .

Water is entering the bucket at the speed that can be calculated as,

$v_{impact} = \sqrt{2 {gy}_{top}}$

Substitute the values, and we get,

$v_{imapact} = \sqrt{2 (9.8 {m/s}^{2}) (2.600 m)} v_{imapact} = 7.14 m/s$

The rate of change of momentum is the force itself:

$\frac{dm}{dt} v_{impact} + F_{extra} \frac{dt}{dt} = \frac{d}{dt} {mv}_{f} \frac{dm}{dt} v_{impact} + F_{extra} = 0$

Substitute the values, and we get,

$F_{extra} = - \frac{dm}{dt} v_{impact} F_{extra} = (- 0.250 kg/s) (- 7.14 m/s) F_{extra} = 1.78 N$

Altogether the scale must exert $= 7.35 N + 7.35 N + 1.78 N = 16.5 N$ .

Thus, the scale read in Newton’s 3.00 s after water starts to accumulate in it is 16.5 N.

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Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Water falls without splashing at a rate of 0.250 L/s from a height of 2.60 m into a bucket on a scale. If the bucket is originally empty, what does the scale read in Newton’s 3.00 s after water starts to accumulate in it?

Step by Step Solution

Step 1: Concept

Step 2: Reading of scale

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Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Water falls without splashing at a rate of 0.250 L/s from a height of 2.60 m into a bucket on a scale. If the bucket is originally empty, what does the scale read in Newton’s 3.00 s after water starts to accumulate in it?

Step by Step Solution

Step 1: Concept

Step 2: Reading of scale

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