Answer Exercise 6.3 .20 when the roller at node 4 allows it to move in only the vertical directi

Answer Exercise 6.3 .20 when the roller at node 4 allows it...

Key Concepts

Structural Equilibrium

Structural equilibrium is a fundamental principle stating that the sum of all forces and moments acting on a structure must be zero for it to remain stable. This concept serves as the basis for analyzing and solving structural systems, guiding the determination of reaction forces and the overall response of the system under load.

Reaction Forces

Reaction forces are the forces that develop at the support points of a structure in response to external loads. Their calculation depends on the type and arrangement of the supports (such as roller, fixed, or pin supports) and the applied boundary conditions, ensuring that the net forces and moments in the structure remain in equilibrium.

Degrees of Freedom

Degrees of freedom refer to the number of independent movements (displacements and rotations) a structure or a joint can exhibit under loading. Recognizing and correctly accounting for the degrees of freedom in structural analysis is essential, as it helps determine the necessary support conditions and influences the overall stability and behavior of the structure.

Roller Support

A roller support is a type of support that restricts movement in one specific direction while allowing free movement in the perpendicular direction. In structural analysis, roller supports typically prevent translation in one axis (usually vertical or horizontal) and permit motion along the other, which influences the reaction forces developed at that support and the overall constraint of the structure.

Boundary Conditions

Boundary conditions are constraints that define how a structure is supported or connected to its surroundings, determining which displacements and rotations are allowed. They are critical in formulating the equations of equilibrium, identifying reaction forces and moments, and ensuring that the structural behavior is accurately modeled and solved.

Transcript

00:01 Cution, it is told that two boxes of the fruits are connected by a light string and it is pulled by a force of 50 newton.

00:09 Now in the first part of the problem we have to find the acceleration and tension in the string.

00:15 And it is told that the surface is frictionless.

00:18 So first of all i am drawing the diagram for this cushion.

00:21 So this is the surface and let this is block of mass that is m1 and this is the block of usmar.

00:30 Is m2 and both are connected by a string and if this mass is pulled by a force that is f is equal to 50 newton now we have given that m1 is 10 kg kilograms m2 is 20 kilograms let the tension in this string is t now in the first part of the problem it is told that the surface is frictionless so we can say that net force is given by in expectation that mass into acceleration so net mass is m1 plus m2 into acceleration in extraction so this is 50 is equal to this is 10 plus 20 into a x so from here we get the value of a x that is 5 by 3 or i can say this will be 1 .67 meter per second is square so this is the acceleration of both block now we have to find the tension so we can say that i'm going to draw the free body diagram of m1 kg block so this is the kg block and on this block there is a tension force t and acceleration of this block is in this direction that is x.

01:50 So we can say that for this t is equal to that is m1 ax.

01:55 So from here this is 10 into 1 .67 or i can say this is 16 .7 newton.

02:01 So tension in the string is 16 .7 newton.

02:06 Now in the second part of the problem it is told that the surface is not friction less and we have given the value of kinetic friction that is is equal to 0 .1...

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