The bar is located on an inclined plane with an angle of inclination of 45. Will the bar be in equilibrium

The bar is located on an inclined plane with an angle of inclination of 45. Will the bar be in equilibrium if the coefficient of friction between the bar and the plane is 0.8.

g = 10 m / s2.

μ = 0.8.

∠α = 45 °.

μ “-?

In order for the bar to be in equilibrium, according to 1 Newton’s law, the action of forces on it must be compensated: Ftr + m * g + N = 0, where Ftr is the sliding friction force, m * g is the force of gravity, N is the reaction force surface of an inclined plane.

ОХ: Ftr – m * g * sinα = 0.

OU: N – m * g * cosα = 0.

Ftr = m * g * sinα.

N = m * g * cosα.

The friction force Ffr is determined by the formula: Ffr = μ “* N = μ” * m * g * cosα.

μ “* m * g * cosα = m * g * sinα.

μ “= m * g * sinα / m * g * cosα = sinα / cosα.

μ “= sin45 ° / cos45 ° = 1.

We see that for the equilibrium of the body, the minimum friction coefficient μ “is μ” = 1.

And we have μ <μ “, the body will slide down the inclined plane.

Answer: the body will slide down an inclined plane.