Question

доска массой 0,4 кг шарнирно подвешена к потолку на легком стержне На доску со скоростью 10 мс налетает пластилиновый шарик и прилипает к ней. Скорость шарика перед ударом направлена под углом 60 градусов к нормали доске. Кинетическая энергия системы тел после соударения равна 0.25Дж. Определите массу шарика​

Answer 1

vx = v0 * cos(a) = 10 * 0,5 = 5 м/с

Дальше по закону сохранения импульса(Обозначим массу доски за М, и массу шарика за м) Формула получится такая:(М м)* v = м * vx Отсюда выразим получившуюся скорость доски с шариком:

v = vx * м / (М м) = 5 * 0,2 / (М 0,2) = 1 / (М 0,2) м/с Поскольку в условии дана получившаяся кинетическая энергия, то образуется такое уравнение: Е = (М м) * v^2 / 2получится: Е = 1/2 * (М 0,2) * 1 / (М 0,2)^2 = 1/2 * 1 / (М 0,2) = 0,625 2 * (М 0,2 ) = 1 / 0,625 = 1,6 М 0,2 = 0,8 М = 0,6 кг.

Ответ: 0,6 кг.

Answer 2

Problem Analysis

We have a board with a mass of 0.4 kg that is hinged to the ceiling by a light rod. A plastic ball collides with the board at an angle of 60 degrees to the normal of the board. After the collision, the kinetic energy of the system of objects is 0.25 J. We need to determine the mass of the ball.

Solution

To solve this problem, we can use the principle of conservation of kinetic energy. Before the collision, the kinetic energy of the ball is given by:

K1 = (1/2) * m * v1^2

where m is the mass of the ball and v1 is its velocity before the collision.

After the collision, the kinetic energy of the system of objects (board and ball) is given by:

K2 = (1/2) * (m + M) * v2^2

where M is the mass of the board, v2 is the velocity of the system after the collision, and (m + M) is the total mass of the system.

Since the board is hinged to the ceiling and the collision is elastic, the board does not move after the collision. Therefore, the velocity of the system after the collision is equal to the velocity of the ball before the collision.

Using the given information that the kinetic energy of the system after the collision is 0.25 J, we can set up the equation:

K2 = (1/2) * (m + M) * v1^2 = 0.25 J

Substituting the values of M = 0.4 kg and v1 = 10 m/s (the initial velocity of the ball), we can solve for m.

Calculation

Let's calculate the mass of the ball using the equation derived above:

(1/2) * (m + 0.4 kg) * (10 m/s)^2 = 0.25 J

Simplifying the equation:

5 * (m + 0.4) = 0.25

5m + 2 = 0.25

5m = 0.25 - 2

5m = -1.75

m = -1.75 / 5

m = -0.35 kg

Answer

The calculated mass of the ball is -0.35 kg. However, a negative mass is not physically meaningful in this context. Therefore, there might be an error in the given information or the calculations. Please double-check the problem statement or provide additional information to resolve the discrepancy.