Question #e406e

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Question #e406e

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Answer 1 · 2015-07-25T17:19:20

I found: $m a s s = 1 \times 10^{- 3} k g$ $mass=1xx10^-3kg$

Explanation:

Considering it as a cylindrical wire you can evaluate its volume $V$ $V$ as:
$V = π r^{2} \times h = 3.14 {(\frac{0.002}{2})}^{2} \times 0.32 = 1 \times 10^{- 6} m^{3}$ $V=pir^2xxh=3.14(0.002/2)^2xx0.32=1xx10^-6m^3$
From:
$d e n i s i t y = \frac{m a s s}{v o l u m e}$ $denisity=(mass)/(volume)$
$m a s s = d e n s i t y \times v o l u m e = 1000 \times 1 \times 10^{- 6} = 1 \times 10^{- 3} k g$ $mass=densityxxvolume=1000xx1xx10^-6=1xx10^-3kg$

Answer 2 · 2015-07-25T17:27:59

Mass of the wire: 1 g

Explanation:

Density is defined as mass per unit of volume.

In your case, the density of the wire is known to be equal to $1000 kg/m^{3}$ $"1000 kg/m"""^3$ , which means that $1 m^{3}$ $"1 m"""^3$ of volume will have a mass of $1000 kg$ $"1000 kg"$ .

So, in order to determine the mass of the wire, you need to know what volume it occupies. You can assume it to have the shape of a very long and thin cylinder, so that tis volume can be determine by using

$V = π \cdot r^{2} \cdot h$ $V = pi * r^2 * h$ , where

$r$ $r$ - the radius of the wire;
$h$ $h$ - its length.

In your case, the wire hs a diameter of 0.002 m, which means that its radius will be

$r = \frac{d}{2} = \frac{0.002 m}{2} = 0.001 m$ $r = d/2 = "0.002 m"/2 = "0.001 m"$

The wire's volume will thus be

$V = π \cdot {(0.001 m)}^{2} \cdot 0.32 m = 1.0 \cdot 10^{- 6} m^{3}$ $V = pi * ("0.001 m")^2 * "0.32 m" = 1.0 * 10^(-6)"m"^3$

This means that the mass of the wire will be

$1.0 * 10^(-6)cancel("m"^3) * "1000 kg"/(1cancel("m"^3)) = 1.0 * 10^(-3)"kg"$

Expressed in grams and rounded to one sig fig, the number of sig figs you gave for the diameter of the wire, the answer will be

$1.0 * 10^(-3)cancel("kg") * (10^3"g")/(1cancel("kg")) = color(green)("1 g")$

Answer 3 · 2015-07-25T17:32:00

1 gram (CGS) or $10^-3$ Kg (SI)

Explanation:

assuming the wire is cylindrical:

Area of the cross section: $pi*r^2$ = $3.14*(0.002/2 )^2=3.14*0.000001=3.14*10^(-6) m^2$

Total volume=area x length: $3.14*10^-6*0.32=1*10^-6m^3$

Total mass=volume x density: $1*10^-6m^3*1000 (Kg)/(m^3)=10^-3Kg=1g$

The numbers were chosen to make the math very simple. The total mass is 1 gram.

Incidentally, this wire is made of a material with the same density as water (real metals are much denser).

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