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Super fine 40-gauge copper wire has a diameter of only and weighs only . Suppose a spool of 40-gauge wire weighs less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used

Sagot :

nuhulawal20

This question is incomplete, the complete question is;

Super fine 40-gauge copper wire has a diameter of only 0.080 mm and weighs only 44.5 g/km. Suppose a spool of 40-gauge wire weighs 205 g less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used ?

Answer: length of wire to be used is 4.6067 km

Explanation:

Circular diameter = d mm

Linear mass density of wire = μ g/km

let m be the mass of wire un-winded from spool to wind a magnet.

If M is mass of wire initially

then

Δm = M - m  { which represents decrease of mass }

Also if L rep the length of wire pulled off,

then

Δm = μ × L grams

⇒ L = Δm/μ km

now given that weight Δm = 205 g and length per unit weight μ = 44.5 g/km

we substitute

L = 205 g  / 44.5 g/km

L =  4.6067 km

Therefore length of wire to be used is 4.6067 km

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