Question

A8Брусок покоится на шероховатой наклонной плоскости (см. рисунок). На него действуют сила тяжести mg, сила упругости опоры N и сила трения Fтр. Чему равен модуль равнодействующей сил Fтр и mg, при условии, что скорость тела не меняется

Answer 1

Он равен N. Из 2 з.н. -N = Fтр+mg. Жирным выделены векторы

Answer 2

Problem Analysis

We have a block resting on a rough inclined plane, and it is subjected to the force of gravity (mg), the normal force (N), and the force of friction (Fтр). We need to determine the magnitude of the resultant force (Fтр + mg) when the velocity of the block is constant.

Solution

To solve this problem, we need to analyze the forces acting on the block and apply Newton's second law of motion.

1. Forces Acting on the Block: - Force of gravity (mg): This force acts vertically downward and is given by the product of the mass of the block (m) and the acceleration due to gravity (g). - Normal force (N): This force acts perpendicular to the inclined plane and is equal in magnitude but opposite in direction to the component of the force of gravity perpendicular to the plane. - Force of friction (Fтр): This force acts parallel to the inclined plane and opposes the motion of the block. Its magnitude depends on the coefficient of friction (μ) and the normal force (N).

2. Newton's Second Law of Motion: According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration. In this case, since the velocity of the block is constant, the acceleration is zero. Therefore, the net force acting on the block must also be zero.

3. Equations: - Net force in the x-direction: Fтр - mg sin(θ) = 0, where θ is the angle of inclination of the plane. - Net force in the y-direction: N - mg cos(θ) = 0.

4. Solving for the Resultant Force: From the equation Fтр - mg sin(θ) = 0, we can solve for Fтр: Fтр = mg sin(θ).

Substituting the value of Fтр into the equation N - mg cos(θ) = 0, we can solve for N: N = mg cos(θ).

Therefore, the magnitude of the resultant force (Fтр + mg) is: Fтр + mg = mg sin(θ) + mg = mg (sin(θ) + 1).

5. Calculation: To calculate the magnitude of the resultant force, we need the values of the mass of the block (m), the acceleration due to gravity (g), and the angle of inclination of the plane (θ).

Unfortunately, the specific values for these variables are not provided in the question. Therefore, we cannot calculate the exact magnitude of the resultant force without this information.

Conclusion

In conclusion, to determine the magnitude of the resultant force (Fтр + mg) acting on the block resting on a rough inclined plane, we need the values of the mass of the block (m), the acceleration due to gravity (g), and the angle of inclination of the plane (θ). Without these values, we cannot calculate the exact magnitude of the resultant force.