Question

С какой минимальной скоростью нужно вращать в вертикальной плоскости ведро с водой, чтобы при прохождении через высшую точку вода из него не вылевалась.Ведро подвешено на верёвке длиной 50 см.

Answer 1

Надо чтобы в верхней точке вода и не давила на дно ведра и не стремилась вниз. Это возможно, когда сила тяжести (и только она) обеспечивает воде нужное центростремительное ускорение. Поэтому

a центростремительное = g
v²/R = g
v = √(gR) =√10*0.5 = 2.23 м/с

Answer 2

Minimum Speed to Rotate a Bucket of Water

To prevent water from spilling out of a bucket when it passes through the highest point, the bucket needs to be rotated at a minimum speed. The minimum speed required can be calculated using the concept of centripetal force and gravitational force.

The minimum speed required to rotate the bucket can be calculated using the formula:

v = √(rg)

Where: - v = minimum speed required (in m/s) - r = length of the rope (in meters) - g = acceleration due to gravity (approximately 9.81 m/s²)

Given that the length of the rope is 50 cm (or 0.5 m), the minimum speed required can be calculated using the above formula.

Calculation

Using the given length of the rope (r = 0.5 m) and the acceleration due to gravity (g = 9.81 m/s²), the minimum speed required can be calculated as follows:

v = √(0.5 * 9.81) v ≈ √4.905 v ≈ 2.214 m/s

Therefore, the minimum speed required to rotate the bucket with water so that it does not spill when passing through the highest point is approximately 2.214 m/s.