Question

A spring with a force constant of 3x10^3 Nm-1 is used to measure the mass of an object. If the spring extends by 5cm when the object is hung from it, the mass of the object is

Answer 1

Hello!

When the object is hung from the spring, the force of the spring balances out the force due to gravity. In terms of equations:

`\Sigma F = F_g - F_s\\\\0 = F_g - F_s\\\\F_s = F_g`

The force of a spring is equivalent to:

`F_s = -kx \\`

k = Spring Constant (3000 N/m)
x = Extension of spring (0.05 m)

**Negative sign means the force is in the opposite direction of the extension. For example, if you pull a spring, the spring force tries to collapse the spring, aka it works against you

The force due to gravity is equivalent to:

`F_g = mg`

m = mass (? kg)
g = acceleration due to gravity (9.81 m/s²)

Solving for mass:

`kx = mg\\\\m = (kx)/(g)\\\\m = (3000(0.05))/(9.81) = \boxed{15.29 kg}`