Question

Find the total mass of two turns of a spring with density ρ in the shape of the circular helix

Answer 1

Step 1 :  

The vector equation of the wire is and .

The wire density is .

Mass of the wire is .

Where .

Compare with .

and .

Substitute and in equation (1).

  

Step 2 : 

Substitute and in .

 Find mass of the wire :

The mass of the wire is .

Solution : 

The mass of the wire is .