From an inclined plane with a height of 0.3 m and a component of 30 ° with the horizon

From an inclined plane with a height of 0.3 m and a component of 30 ° with the horizon, a ball rolls without sliding. Ignoring friction, determine the time of the ball movement along the inclined plane.

From the condition of the problem it is known that with an inclined plane with a height of h = 0.3 m and making an angle α = 30 ° with the horizon, a ball rolls without sliding. Then the length of the inclined plane or the path traversed by the ball will be S = 2 ∙ h = 2 ∙ 0.3 = 0.6 (m) – according to the property of the leg, which lies opposite the angle α = 30 °.

On the other hand, the path traversed by a ball moving in a straight line and uniformly accelerated is determined by the formula: S = a ∙ t² / 2. then the time of movement will be: t² = 2 ∙ S / a. Acceleration a is found from Newton’s second law, according to the law the resultant is F = m ∙ a or m ∙ a = m ∙ g ∙ sinα; a = g ∙ sinα, where the proportionality coefficient is g = 9.8 N / kg, and friction is neglected.

Let’s substitute the values ​​of physical quantities in the calculation formula and find the time of the ball’s movement: t² = 2 ∙ 0.6 / (9.8 ∙ 0.5); t ≈ 0.5 s.

Answer: the time for the ball to move along an inclined plane is 0.5 seconds.