A body without an initial velocity slides with an area curve. The angle of inclination of the area

| May 13, 2021 | education

A body without an initial velocity slides with an area curve. The angle of inclination of the area to the horizon is 30 °, the length of the inclined plane is 2m. With what acceleration does the body move if the coefficient of friction is 0.3. How long does speed last?

Problem data: α (slope of the curved plane) = 30º; l (length of the inclined plane) = 2 m; μ (coefficient of friction) = 0.3.

Constants: g (acceleration due to gravity) ≈ 10 m / s2.

1) Find the acceleration of the body on an inclined plane: ОХ: m * a = Fт * sinα – Fтр = m * g * sinα – μ * m * g * cosα, whence we express: a = g * sinα – μ * g = 10 * sin 30º – 0.3 * 10 * cos 30º = 2.4 m / s2.

2) Calculate the duration of the movement: S = a * t ^ 2/2, whence we express: t = √ (2S / a) = √ (2 * 2 / 2.4) = 1.29 s.

Answer: The body moved along a given inclined plane with a constant acceleration of 2.4 m / s2 for 1.29 s.



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