Solution of problem 5.1.4 from the collection of Kepe O.E.

5.1.4 The moment of force F relative to the center O is equal to Mo (F) = 100 N m and is located in space so that the angles ?=30° and ?=30°. Determine the moment of this force relative to the Oy axis. (Answer 25)

Given: moment of force relative to the center O - Mo (F) = 100 N m, angles ?=30° and ?=30°.

Find: the moment of this force relative to the Oy axis.

Answer:

The moment of force F relative to the Oy axis can be found by the formula Mu (F) = F * d, where F is the force, d is the distance from the Oy axis to the line of action of the force F.

To find the force F and distance d, it is necessary to expand the force F into projections on the Ox, Oy and Oz axes.

According to the conditions of the problem, the angles ?=30° and ?=30°, therefore, the force F will have projections on the Ox, Oy and Oz axes equal to Fx = F * cos(30°), Fy = F * cos(30°) and Fz = F * sin(30°).

Since the force F is directed in a plane passing through the Oy axis and the center O, the distance d from the Oy axis to the line of action of the force F will be equal to the distance from the center O to the projection of the force F onto this plane, that is, d = R * cos(30 °), where R is the distance from the center O to the point of application of force F.

Thus, the moment of force F relative to the Oy axis will be equal to:

Mу (F) = Fy * d = (F * cos(30°)) * (R * cos(30°)) = F * R * cos²(30°) = 100 * cos²(30°) ≈ 25 Н·м.

Answer: the moment of this force relative to the Oy axis is equal to 25 N m.

Solution to problem 5.1.4 from the collection of Kepe O.?.

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Digital product "Solution to problem 5.1.4 from the collection of Kepe O.?." is a detailed description of the process of solving a problem from general physics. The task is to determine the moment of force F relative to the Oy axis, provided that the moment of force relative to the center O is equal to 100 N·m, and the angles ?=30° and ?=30°.

The digital product contains all the necessary formulas and calculations that make it easy to understand and repeat the solution to the problem. The solution is provided in a convenient HTML format that can be viewed on any device. The beautiful design of the solution makes it more attractive and convenient to use.

This product can be useful to both students and teachers studying general physics. By purchasing this digital product, you receive a reliable and comprehensive source of information that will help you better understand general physics material and solve problems successfully.

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Solution to problem 5.1.4 from the collection of Kepe O.?. consists in determining the moment of force F relative to the Oy axis based on the available data. From the conditions of the problem it is known that the moment of force F relative to the center O is equal to 100 N m and the angles between the force vector and the axes Ox and Oy are equal to 30°.

To solve the problem, you need to use the formula to calculate the moment of force:

M = F * d,

where M is the moment of force, F is force, d is the distance from the axis of rotation to the line of action of the force.

To determine the moment of force relative to the Oy axis, it is necessary to find the projection of the force vector onto the Oy axis and multiply it by the distance to the Oy axis.

Since the angles between the force vector and the Ox and Oy axes are equal to 30°, it is possible to calculate the projections of the force vector on the Ox and Oy axes using trigonometric functions:

Fх = F * cos 30°, Fу = F * sin 30°.

The distance from the center O to the Oy axis is zero, since the Oy axis passes through the center O. Thus, the moment of force relative to the Oy axis is equal to:

Mu = Fu * 0 = 0.

Answer: 0.

Solution to problem 5.1.4 from the collection of Kepe O.?. is as follows: given the equation of a straight line on a plane in the form ax + by + c = 0 and a point with coordinates (m, n). It is necessary to find the distance from this point to the line.

To solve the problem, you can use the formula for the distance from a point to a line, which is expressed as the modulus of the ratio of the value of the expression ax + by + c to the root of the sum of the squares of the coefficients a and b. Thus, the distance d from the point (m, n) to the straight line ax + by + c = 0 will be equal to:

d = |am + bn + c| / √(a^2 + b^2)

It is only necessary to substitute the values ​​of the coefficients a, b, and c from the equation of the line, as well as the coordinates of the point (m, n) into this formula and calculate the distance d.

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