What is the coefficient of friction of the bar on an inclined plane, if the bar slides with an acceleration of 1 m / s ^ 2

What is the coefficient of friction of the bar on an inclined plane, if the bar slides with an acceleration of 1 m / s ^ 2, the angle of inclination of the plane is 30 degrees.

Given:

a = 1 m / s ^ 2 – acceleration with which the bar slides off the inclined plane;

g = 10 m / s ^ 2 – acceleration of gravity;

a = 30 degrees – the angle of inclination of the plane to the horizon.

It is required to find the coefficient of friction k.

It is clear from the problem statement that the bar slides off under the action of gravity. Then, according to Newton’s second law:

F gravity – F friction = m * a.

Taking into account the decomposition of forces into directions along the inclined plane and perpendicular to it, we obtain:

m * g * sin (a) – k * m * g * cos (a) = m * a;

g * sin (a) – k * g * cos (a) = a;

k * g * cos (a) = g * sin (a) – a;

k = (g * sin (a) – a) / (g * cos (a)) = (10 * 0.5 – 1) / (10 * 0.9) = (5 – 1) / 9 = 4 / 9 = 0.4

Answer: the coefficient of friction of the bar on the inclined plane is 0.4.