Question

Небольшой шарик, прикрепленный к нити длиной L = 0,4 м, движется по окружности в вертикальной плоскости. Скорость шарика при прохождении нижнего положения v = 6 м/с. Найти ускорение шарика в верхней точке траектории. Нить считать нерастяжимой. Принять g = 10 м/с2.

Answer 1

Из закона сохранения энергии

Answer 2

Problem Analysis

We are given a small ball attached to a string of length L = 0.4 m, moving in a vertical plane in a circular path. The ball's velocity at the bottom position is v = 6 m/s. We need to find the acceleration of the ball at the top point of the trajectory. The string is assumed to be inextensible, and the acceleration due to gravity is g = 10 m/s^2.

Solution

To find the acceleration of the ball at the top point of the trajectory, we can use the centripetal acceleration formula. The centripetal acceleration is the acceleration directed towards the center of the circular path.

The centripetal acceleration can be calculated using the formula:

a = v^2 / r

where: - a is the centripetal acceleration - v is the velocity of the ball - r is the radius of the circular path

In this case, the radius of the circular path is equal to the length of the string, L.

Let's substitute the given values into the formula and calculate the acceleration.

Calculation

Given: - Length of the string, L = 0.4 m - Velocity of the ball at the bottom position, v = 6 m/s - Acceleration due to gravity, g = 10 m/s^2

Using the formula for centripetal acceleration:

a = v^2 / r

Substituting the values:

a = (6 m/s)^2 / 0.4 m

Simplifying:

a = 36 m^2/s^2 / 0.4 m

a = 90 m/s^2

Therefore, the acceleration of the ball at the top point of the trajectory is 90 m/s^2.

Answer

The acceleration of the ball at the top point of the trajectory is 90 m/s^2.