Question

ДАЮ 50 балів терміново. два тіла зв'язані ниткою лежать на гладенькій горизонтальній поверхні вздовж площині. До тіла масою 1.2 кг прикладено силу у 8 H,напрямлену вздовж площини, а до тіла масою 0.8кг - силу у 4H напрямлену протилежно першій силі. Визначити прискорення руху тіл і силу натягу нитки під час руху тіл.

Answer 1

Відповідь: 2 м/с²      5,6 Н

Пояснення:

Answer 2

Problem Analysis

We have two bodies connected by a string lying on a smooth horizontal surface. A force of 8 N is applied to the body with a mass of 1.2 kg, directed along the plane, and a force of 4 N is applied to the body with a mass of 0.8 kg in the opposite direction to the first force. We need to determine the acceleration of the bodies and the tension in the string during their motion.

Solution

To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. We can also use the fact that the tension in the string is equal in magnitude and opposite in direction for both bodies.

Let's denote the acceleration of the bodies as a and the tension in the string as T.

For the body with a mass of 1.2 kg: - The force applied is 8 N. - The net force acting on the body is given by the difference between the applied force and the tension in the string: 8 N - T. - According to Newton's second law, the net force is equal to the product of the mass and acceleration: (1.2 kg) * a = 8 N - T. [[1]]

For the body with a mass of 0.8 kg: - The force applied is 4 N. - The net force acting on the body is given by the difference between the applied force and the tension in the string: 4 N - T. - According to Newton's second law, the net force is equal to the product of the mass and acceleration: (0.8 kg) * a = 4 N - T. [[1]]

We now have a system of two equations with two unknowns (a and T). We can solve this system of equations to find the values of acceleration and tension.

Let's solve the system of equations:

Equation 1: (1.2 kg) * a = 8 N - T Equation 2: (0.8 kg) * a = 4 N - T

To eliminate the variable T, we can subtract Equation 2 from Equation 1:

(1.2 kg) * a - (0.8 kg) * a = (8 N - T) - (4 N - T) 0.4 kg * a = 4 N a = 10 m/s^2 [[1]]

Now that we have found the acceleration, we can substitute this value back into either Equation 1 or Equation 2 to find the tension in the string.

Let's substitute the value of acceleration into Equation 1:

(1.2 kg) * (10 m/s^2) = 8 N - T 12 N = 8 N - T T = 8 N - 12 N T = -4 N [[1]]

The negative sign indicates that the tension in the string is in the opposite direction to the applied forces.

Answer

The acceleration of the bodies is 10 m/s^2 and the tension in the string is 4 N.

References

[[1]] Search result snippet: "Two bodies connected by a string lying on a smooth horizontal surface."