Respuesta :
Answer:
The relation between [tex]W_{1} \ and \ W_{2}[/tex] is [tex]W_{2} = 3 \ W_{1}[/tex]
Step-by-step explanation:
Natural length = 0.23 m
Spring stretches from 23 cm to 33 cm. now
Work done [tex]W_{1}[/tex] in stretching the spring
[tex]W_{1} = \int\limits^a_b {kx} \, dx[/tex]
where b = 0 & a = 0.1 m
[tex]W_{1} = k [\frac{x^{2} }{2} ][/tex]
With limits b = 0 & a = 0.1 m
Put the values of limits we get
[tex]W_{1} = k [\frac{0.1^{2} }{2} ][/tex]
[tex]W_{1} = 0.005 k[/tex] ------- (1)
Now the work done in stretching the spring from 33 cm to 43 cm.
[tex]W_{1} = \int\limits^a_b {kx} \, dx[/tex]
With limits b = 0.1 m to a = 0.2 m
[tex]W_{2} = k [\frac{x^{2} }{2} ][/tex]
With limits b = 0.1 m to a = 0.2 m
[tex]W_{2} = k [\frac{0.2^{2} - 0.1^{2} }{2} ][/tex]
[tex]W_{2} =0.015[/tex]
[tex]\frac{W_{2} }{W_{1} } = \frac{0.015}{0.005}[/tex]
[tex]\frac{W_{2} }{W_{1} } =3[/tex]
Thus
[tex]W_{2} = 3 \ W_{1}[/tex]
This is the relation between [tex]W_{1} \ and \ W_{2}[/tex].
