Question

К нижнему концу легкой пружины подвешены связанные невесомой нитью грузы:верхний массой m1 = 0,5 кг и нижний массой m2 = 0,2 кг.Нить, соединяющей грузы,переживают. Определить проекцию ускорения на направленную вниз ось OY, с которым начнёт двигаться верхний груз.

Answer 1

В начальный момент времени
(m1+m2)*a=(m1+m2)*0=(m1+m2)*g-k*x0
x0=(m1+m2)*g/k
при пережигании нити
m1*a=m1*g-k*х
a=g-k*х/m1
в начальный момент х=х0
в начальный момент a=g-k*х0/m1=g-k*((m1+m2)*g/k)/m1=
=g*(1-(m1+m2)/m1)=-m2/m1*g
ответ
а=-m2/m1*g
ускорение со знаком минус - направлено вверх

Answer 2

Calculation of the Acceleration

To determine the projection of the acceleration on the downward OY axis with which the upper mass will start moving, we can use Newton's second law of motion. According to this law, the net force acting on an object is equal to the product of its mass and acceleration.

In this case, the net force acting on the system is the tension in the string. The tension in the string is the same throughout its length, so we can consider the tension acting on the upper mass as the net force.

Let's denote the tension in the string as T. The net force acting on the upper mass (m1) is T, and the mass of the upper mass is m1 = 0.5 kg.

According to Newton's second law, we have:

T = m1 * a

where a is the acceleration of the upper mass.

Now, let's consider the forces acting on the upper mass. We have the tension T acting upward and the weight of the upper mass (m1 * g) acting downward, where g is the acceleration due to gravity.

Since the upper mass is moving downward, the net force acting on it is the difference between the tension and the weight:

T - m1 * g = m1 * a

We can rearrange this equation to solve for the acceleration a:

a = (T - m1 * g) / m1

Now, let's substitute the given values into the equation:

m1 = 0.5 kg g = 9.8 m/s^2 (acceleration due to gravity)

To determine the tension T, we need more information about the system, such as the length of the string or any additional forces acting on the system. Without this information, we cannot calculate the exact value of the acceleration or tension.

Please provide more details about the system or any additional forces acting on it so that we can assist you further.