A wooden block is pulled along a wooden board placed horizontally using a spring of 100 N / m.

| February 6, 2021 | education

A wooden block is pulled along a wooden board placed horizontally using a spring of 100 N / m. Friction coefficient 0, 2. find the mass of a bar if the spring elongation is 0.05 m, and the bar moves with an acceleration of 0.5 m / s ^ 2

x = 0.05 m.

μ = 0.2.

g = 9.8 m / s2.

k = 100 N / m.

a = 0.5 m / s2.

m -?

Let’s write 2 Newton’s law: m * a = F + Ftr + m * g + N.

Let’s write 2 Newton’s law for projections on the coordinate axes.

ОХ: m * a = F – Ftr.

OU: 0 = N – m * g.

We find the force F with which the bar is pulled according to Hooke’s law: F = k * x.

N = m * g.

The friction force is determined by the formula: Ftr = μ * N = μ * m * g.

m * a = k * x – μ * m * g.

We find the mass of the bar by the formula: m = k * x / (a + μ * g).

m = 100 N / m * 0.05 m / (0.5 m / s2 + 0.2 * 9.8 m / s2) = 2.6 kg.

Answer: a wooden block has a mass of m = 2.6 kg.



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