A0.76-kg block is hung from and stretches a spring that is attached to the ceiling. a second block is attached to the first one, and the amount that the spring stretches from its unstretched length triples. what is the mass of the second block?

1.54 kg

Explanation:

mass of first block (m) = 0.76 kg

acceleration due to gravity (g) = 9.8 m/s

what is the mass (m) of the second block

        mg = kx

        where m is the mass, g is the acceleration due to gravity, k is the  

        spring constant and x is the extension

        0.76 x 9.8 = kx

       7.5 = kx

        k = 7.5/x ... equation 1

        therefore the new mass becomes m + 0.76 and the extension  

        becomes 3x

        with the new mass and extension, mg = kx now becomes

        (m+0.76)g = k(3x) ... equation 2

        Recall that k = 7.5/x from equation 1, substituting this value of k into      

        equation 2 we have

         (m+0.76)g =   × (3x)

         (m+0.76)g =  7.5 × 3

          substituting the value of g = 9.8 m/s^{2}

         (m + 0.76) x 9.8 = 7.5 x 3

          m + 0.76 = 22.5 ÷ 9.8

          m + 0.76 = 2.3

          m = 2.3 - 0.76 = 1.54 kg

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