Question #e406e

3 Answers
Jul 25, 2015

Answer:

I found: #mass=1xx10^-3kg#

Explanation:

Considering it as a cylindrical wire you can evaluate its volume #V# as:
#V=pir^2xxh=3.14(0.002/2)^2xx0.32=1xx10^-6m^3#
From:
#denisity=(mass)/(volume)#
#mass=densityxxvolume=1000xx1xx10^-6=1xx10^-3kg#

Jul 25, 2015

Answer:

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#, which means that #"1 m"""^3# of volume will have a mass of #"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 = pi * r^2 * h#, where

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

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

#r = d/2 = "0.002 m"/2 = "0.001 m"#

The wire's volume will thus be

#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")#

Jul 25, 2015

Answer:

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).