Question

A 0.76-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?

Answer 1

1.54 kg

Step-by-step 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

• force = kx ⇒ mg = kx

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

• when a second block is attached to the first one the amount of stretch triples (this means that extension (x) = 3x)

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 =
`(7.5)/(x)` × (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