A weight weighing m = 100 g hangs on a spring with a stiffness k = 10 N / m. After the spring with a weight

A weight weighing m = 100 g hangs on a spring with a stiffness k = 10 N / m. After the spring with a weight was lowered into the water, the length of the spring changed by Δl = 4 cm. Determine the density of the material from which the weight is made.

k = 10 N / m.

g = 10 m / s2.

m = 100 g = 0.1 kg.

Δl = 4 cm = 0.04 m.

ρ0 = 1 g / cm3 = 1000 kg / m3.

ρ -?

m * g = k * x – the condition for the balance of the load in the air.

The buoyancy force of Archimedes Farkh acts on the load in the water, directed vertically upward, so the length of the spring will decrease by Δl.

The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρ0 * g * V. Where ρ0 is the density of water, g is the acceleration of gravity, V is the volume of the immersed part of the body in the liquid.

m * g = k * x1 + Farch – the condition for the balance of the load in the water.

We subtract the second from the first equation: 0 = k * x – k * x1 – Farch.

Farch = k * x – k * x1.

Farch = k * (x – x1) = k * Δl.

ρ0 * g * V = k * Δl.

V = k * Δl / ρ0 * g.

V = 10 N / m * 0.04 m / 1000 kg / m3 * 10 m / s2 = 0.0004 m3.

The density of the body ρ is expressed by the formula: ρ = m / V.

ρ = 0.1 kg / 0.0004 m3 = 250 kg / m3 = 0.25 g / cm3 = 3 g / cm3.

According to the density table of substances, we see that the weight is made of cork.

Answer: the load is made of cork ρ = 0.3 g / cm3.