Solution to problem 2.4.38 from the collection of Kepe O.E.

Let us solve the problem of determining the moment in embedding A in kN m, if the following parameters are known: force F = 80 kN, angle? = 30°, distance to the point of application of force l1 = 1.8 m, distance from point of application of force to the embedment l2 = 2 m, and height h = 0.4 m.

Answer:

Let's calculate the projections of force F on the x and y axes:

Fx = F * cos(?), Fy = F * sin(?)

Projection values: Fx = 69.282 kN, Fy = 39.139 kN

Let's calculate the moment of force F relative to the embedment A:

M = Fy * l1 + Fx * h - Fy * l2

Let's substitute the known values:

M = 39.139 * 1.8 + 69.282 * 0.4 - 39.139 * 2 = 35.7 kN·m

Answer: 35.7 kN m

Solution to problem 2.4.38 from the collection of Kepe O..

We present to your attention the solution to problem 2.4.38 from the collection “Problems in Theoretical Mechanics” by the author O.. Kepe. This digital product contains a detailed solution to the problem that will help you better understand the theoretical foundations of mechanics and prepare for exams.

You will receive information on how to determine the moment in the embedment A in kN m if the parameters of force F, angle ?, distances l1 and l2, and height h are known. All material is designed in beautiful html markup, which will make the solution easier to read and understand.

By purchasing this digital product, you gain access to useful information that will be useful for both beginners and experienced students and experts in the field of mechanics.

A digital product is offered - a solution to problem 2.4.38 from the collection "Problems in Theoretical Mechanics" by author O.?. Kepe. In this problem, it is required to determine the moment in the embedment A in kN m if the parameters of force F, angle θ, distances l1 and l2, and height h are known.

To solve the problem, it is necessary to calculate the projections of the force F on the x and y axes using the formulas Fx = F * cos(?) and Fy = F * sin(?). Then calculate the moment of force F relative to the embedment A, using the formula M = Fy * l1 + Fx * h - Fy * l2.

The resulting result must be expressed in kN m. In this problem, the answer is 35.7 kN m.

By purchasing this digital product, you will get access to a detailed solution to the problem, which will help you better understand the theoretical foundations of mechanics and prepare for exams. The solution is presented in beautiful html markup, which will make the material easier to read and understand. This product can be useful for both beginners and experienced students and specialists in the field of mechanics.

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Solution to problem 2.4.38 from the collection of Kepe O.?. consists in determining the moment in seal A under given conditions.

The following known quantities are given in the problem:

• force F = 80 kN, directed at an angle? = 30° to the horizon;
• distance from the point of application of force F to the embedment A l1 = 1.8 m;
• the distance from the embedment A to the point of intersection of the continuation of the line of action of the force F with the vertical l2 = 2 m;
• the height of the point of intersection of the continuation of the line of action of force F with the vertical above the embedding h = 0.4 m.

To solve the problem, you need to calculate the moment of force F relative to the embedment A. To do this, we use the formula for the moment of force:

M = F * l,

where F is the force, l is the distance from the point of application of the force to the axis of rotation (in this case, to embedment A).

To calculate l, we use the cosine theorem for the triangle formed by the vectors F, l1 and l2:

l^2 = l1^2 + l2^2 - 2 * l1 * l2 * cos(?),

Where ? - angle between vectors F and l1.

We substitute the known values ​​and find l:

l^2 = 1,8^2 + 2^2 - 2 * 1,8 * 2 * cos(30°) = 4,67 м^2,

l = sqrt(4.67) = 2.16 m.

Now we can calculate the moment of force:

M = 80 kN * 2.16 m * sin(30°) = 35.7 kN·m.

Answer: the moment at embedment A is 35.7 kN m.

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