Solution to problem 3.2.8 from the collection of Kepe O.E.

3.2.8 Rods ABC and CD are connected to each other by hinge C. Rod CD is acted upon by a pair of forces with a moment M = 400 N m. Determine the component Xc of the reaction of the hinge C, if the length CD = 2 m. (Answer 200)

Answer:

In this problem, in order to find the component Xc of the reaction of the hinge C, it is necessary to use the moments of forces. Since the rod CD is connected to the hinge C, the reaction of the hinge C will act in the direction of this rod. Let's find the moment of a pair of forces acting on the rod CD:

M = 400 Nm

The length of the rod CD is 2 m. Since the pair of forces acts perpendicular to the rod CD, the moment of this pair of forces is equal to:

M = F·l

where F is the force acting on the rod CD, l is the length of the rod CD.

From here:

F = M / l = 400 N·m / 2 m = 200 N

Thus, the component Xc of the reaction of hinge C is equal to 200 N.

Solution to problem 3.2.8 from the collection of Kepe O..

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We bring to your attention the solution to problem 3.2.8 from the collection of Kepe O.?. in mechanics. The task is to determine the component Xc of the reaction of the hinge C connecting the rods ABC and CD, if the rod CD is acted upon by a pair of forces with a moment M = 400 N m, and the length CD is 2 m.

The solution to the problem is based on the use of moments of forces. Since hinge C is connected to rod CD, the reaction of hinge C will act in the direction of this rod. It is necessary to find the force acting on the rod CD in order to calculate the Xc component of the reaction of the hinge C.

The moment of the pair of forces acting on the rod CD is equal to M = 400 N·m. Since the pair of forces acts perpendicular to the rod CD, the moment of this pair of forces is equal to F·l, where F is the force acting on the rod CD, l is the length of the rod CD.

Thus, the force F is equal to F = M / l = 400 N m / 2 m = 200 N. The Xc component of the reaction of the hinge C is equal to 200 N.

Our solution is presented in the form of a convenient HTML document that can be opened on any device connected to the Internet. The document contains detailed step-by-step instructions for solving the problem, as well as formulas and calculations necessary to correctly solve the problem. By purchasing our solution, you save your time and get guaranteed results.

Don't miss the opportunity to successfully complete the task and get a high grade - purchase our solution to problem 3.2.8 from the collection of Kepe O.?. today!

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Solution to problem 3.2.8 from the collection of Kepe O.?. consists in determining the component Xc of the reaction of the hinge C under the action of a pair of forces on the rod CD with a moment M = 400 N m and a length CD = 2 m.

To solve the problem, you can use the moments of forces acting on hinge C. Since hinge C cannot transmit moments to forces acting on rod CD, the moment of this pair of forces must be balanced by the moment of reaction of hinge C.

The reaction moment of the hinge C can be expressed through the component Xc of this reaction and the distance from the hinge C to the line of action of the pair of forces on the rod CD. These parameters are known and equal, respectively: M = 400 N m and CD = 2 m.

Using the formula for the moment of force M = F * l * sin(α), where F is the force, l is the distance from the point of application of the force to the axis of rotation, α is the angle between the force vector and the radius vector from the axis of rotation to the point of application of the force, we can express the component Xc of the reaction of the hinge C:

M = Xс * CD * sin(90°)

Xs = M / (CD * sin(90°)) = 400 N·m / (2 m * 1) = 200 N.

Thus, the component Xc of the reaction of hinge C is equal to 200 N.

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