Question

A 0.47-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

The mass of the second block is 0.94 kg

Step-by-step explanation:

Given;

mass of the first block, m₁ = 0.47 kg

let the mass of the first block and second block = m₂

According to Hook's law;

F = kx

where;

F is the applied load (force)

k is the elastic constant

x is the extension of the elastic material

According to Newton's law of motion;

F = ma = mg

Thus,

mg = kx

`k = (mg)/(x) \\\\(m_1g)/(x_1) = (m_2g)/(x_2) \\\\But, x_2 \ is \ triple \ of \ x_1,\\x_2 = 3x_1\\\\(m_1g)/(x_1) = (m_2g)/(3x_1)\\\\(m_1)/(x_1) = (m_2)/(3x_1)\\\\Substitute \ in \ the \ value \ of \ m_1\\\\(0.47)/(x_1) = (m_2)/(3x_1)\\\\(0.47)/(1) = (m_2)/(3)\\\\m_2 = 3 *0.47\\\\m_2 = 1.41 \ kg`

mass of the second block alone = 1.41 - 0.47 = 0.94 kg

Therefore, the mass of the second block is 0.94 kg