The pendulum is in equilibrium under the influence of a pair of forces

First, let's define the data: the pendulum is in equilibrium under the action of two pairs of forces. The first pair of forces has a moment M = 0.5 N*m, and the second pair of forces is formed by the weight G and the support reaction R. The values ​​are known: G = 10 N and distance l = 0.1 m. It is necessary to find the value of the angle f of the pendulum's deflection in degrees.

To solve the problem, we use the equilibrium condition of the pendulum: the sum of the moments of forces acting on the pendulum must be equal to zero.

The moment of the first pair of forces is equal to M = 0.5 Nm. The moment of the second pair of forces can be found, taking into account that the pendulum is in equilibrium: the moment of the weight is equal to the moment of the support reaction, that is, G * l = R * l. This means that the moment of the second pair of forces is equal to G * l = 10 N * 0.1 m = 1 Nm.

Thus, the sum of the moments of forces is equal to M + G * l = 0.5 Nm + 1 Nm = 1.5 N*m.

In order to find the value of the angle φ, we use the formula for the moment of force: M = F * l * sin(φ), where F is the force, l is the distance from the point of application of the force to the axis of rotation, and sin(φ) is the sine of the angle deviations.

Using this formula, you can find the angle of deflection of the pendulum: sin(ф) = M / (F * l) = 1.5 Nm / (G * l) = 1.5 Nm / (10 N * 0.1 m) = 1.5 rad. Therefore, the angle of deflection of the pendulum is φ = 1.5 rad * 180/π ≈ 85.94 degrees.

Thus, the value of the pendulum's deflection angle is about 85.94 degrees.

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This digital product is a fascinating problem on a physical topic, describing a pendulum in equilibrium under the influence of two pairs of forces. The first pair of forces has a moment M = 0.5 N*m, and the second pair of forces is formed by the weight G and the support reaction R. The values ​​are known: G = 10 N and distance l = 0.1 m. It is necessary to find the value of the angle f of the pendulum's deflection in degrees.

The problem uses the equilibrium condition of a pendulum: the sum of the moments of forces acting on the pendulum must be equal to zero. The moment of the first pair of forces is equal to M = 0.5 Nm. The moment of the second pair of forces can be found, taking into account that the pendulum is in equilibrium: the moment of the weight is equal to the moment of the support reaction, that is, G * l = R * l. This means that the moment of the second pair of forces is equal to G * l = 10 N * 0.1 m = 1 Nm. Therefore, the sum of the moments of force is equal to M + G * l = 0.5 Nm + 1 Nm = 1.5 N*m.

To find the value of the pendulum deflection angle φ in degrees, the formula for the moment of force is used: M = F * l * sin(φ), where F is the force, l is the distance from the point of application of the force to the axis of rotation, and sin(φ) is the sine of the angle deviations. Using this formula, you can find the angle of deflection of the pendulum: sin(ф) = M / (F * l) = 1.5 Nm / (G * l) = 1.5 Nm / (10 N * 0.1 m) = 1 .5 rad. Therefore, the angle of deflection of the pendulum is φ = 1.5 rad * 180/π ≈ 85.94 degrees.

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This product is a description of the solution to problem 11209, which involves a pendulum in equilibrium under the action of a pair of forces.

According to the conditions of the problem, the pendulum is in equilibrium under the action of two pairs of forces: the first pair of forces creates a moment M = 0.5 N*m, and the second pair of forces is formed by the weight G = 10 N and the support reaction R.

The task is to find the value of the pendulum deflection angle φ in degrees for given parameters, including the distance l = 0.1 m.

To solve the problem, it is necessary to use the laws of mechanics and formulas related to the pendulum and the balance of forces. The calculation formula for finding the angle φ will be derived at each step of solving the problem.

If you have any questions about the solution to the problem or the formulas used in the solution, please do not hesitate to ask for help.

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