Answer:
[tex]s = \frac{3}{10}m[/tex]
Step-by-step explanation:
Given
Mass = 30g
Spring Stretch = 9cm
Variation: Direct Variation
Required
Equation that relates the mass of the object, m, and the length of the spring, s
Let m represents mass and s represents length of the spring
Given that s varies directly to m;
This implies that
[tex]s\ \alpha\ m[/tex]
Convert the above to an equation
[tex]s = km[/tex]; where k is the constant of variation;
The next step is to solve for k
Divide both sides by m
[tex]\frac{s}{m} = \frac{km}{m}[/tex]
[tex]\frac{s}{m} = k[/tex]
[tex]k = \frac{s}{m}[/tex]
From the given parameters;
when m = 30; s = 9.
[tex]k = \frac{9}{30}[/tex]
Divide the numerator and denominator by 3
[tex]k = \frac{3}{10}[/tex]
To get the equation that relates the mass of the object to the length of the spring
Substitute [tex]k = \frac{3}{10}[/tex] in [tex]s = km[/tex]
This becomes
[tex]s = \frac{3}{10}m[/tex]
Hence, the equation that relates the mass and length is [tex]s = \frac{3}{10}m[/tex]
