Question

The top of the folding workbench has a mass of 50 kg with mass center at G. Calculate the x- and -y components of the force supported by the pin at E

 

The top of the folding workbench has a mass of 50 kg with mass center at G. Calculate the x- and -y components of the force supported by the pin at E

Answer 1

Concepts and reason

The reactions forces at the supports can be calculated by using force equilibrium equations along horizontal and vertical direction, and moment equilibrium equation.

The major assumption for applying these equilibrium equations is that the body remains rigid.

Before applying these equilibrium equations, distinction should be made between the known and unknown forces that act on the body. When all the supports are removed by replacing them with forces that prevents the translation of body in a given direction, that diagram is called free body diagram.

The equations of the equilibrium are generally used when the bodies are in static equilibrium.

Fundamentals

Force is a vector quantity. It is represented by a magnitude, direction, and point of application.

The direction of force can be either compressive or tensile.

Magnitude of moment can be calculated by multiplying the magnitude of force with the perpendicular distance between the point where the force is applied and the point where the moment to be found.

A body is in equilibrium if vector sum of all the forces is equal to zero or moment of all forces about any point is equal to zero. That is,

Summation of all forces in x direction is zero,

Summation of all forces in y direction is zero,

Moment about arbitrary point is zero,

General sign convention for moment: The moment is considered positive in counter-clockwise direction and negative in clockwise direction.

Draw the free body diagram of the workbench.

Apply moment equilibrium equation about point D.

Here, the vertical reaction force at point B is and mass of the work bench is m, and the acceleration due tor gravity is g.

Substitute for m and for g.

Apply force equilibrium equation along the vertical direction.

Here, the vertical reaction force at support D is .

Substitute for , for m, and for g.

Draw the free body diagram of the bars AB and CD.

Owing to symmetry of the entire assembly, the forces at A and D are equal and also forces at B and C are equal.

Substitute for and for .

Here, the vertical reaction force at support A and C are and respectively.

Draw the free body diagram of the single bar AB.

Apply moment equilibrium equation about point E.

Substitute for and for .

Apply force equilibrium equation along the horizontal direction.

Here, the horizontal reaction force at support E is .

Substitute for .

Apply force equilibrium equation along the vertical direction.

Here, the vertical reaction force at support E is .

Substitute for and for .

Ans:

The magnitude of the force that can be supported by the pin E along the horizontal direction is .

The magnitude of the force that can be supported by the pin E along the vertical direction is .