A 0.70-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 unstrained length triples. What is the mass of the second block?

Respuesta :

Answer:

Mass of the second block is 1.4 kg

Explanation:

When a weight (mg) is displaced from its equilibrium position in a spring mass system, a restoring force (kx) will act on the weight.

so, mg = -kx

where, k is a constant

Mass of block ([tex]m_1[/tex]) = 0.70 kg

For one spring mass system,

[tex]m_1g=-kx_1[/tex]

For the two spring mass system,

[tex]m_2g+m_2g=-kx_2[/tex]

divide equation 2 by 1

[tex]\frac{m_1g+m_2g}{m_1g} =\frac{-Kx_2}{-kx_1}[/tex]

[tex]1+\frac{m_2}{m_1} =\frac{x_2}{x_1}[/tex]

on further rearranging,

[tex]m_2=m_1(\frac{x_2}{x_1} -1)\\=(0.70\ kg)\times (3.0 - 1)\\=1.4\ kg[/tex]

So, mass of the second block is 1.4 kg.