Well, yes, it's not really a 3D problem.mcrooster said:
The component has a x y z, does that not make it 3d with there being 3 axis.haruspex said:
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You did not answer my question. There are two applied forces F, same magnitude but different directions. What is the resultant of those two?mcrooster said:
Sorry for the late reply. Would Fr not be the sum of all forces which is 4cos30+4sin30+4cos30+4sin30 = 11haruspex said:
4cos30 is the magnitude of the X component of one of the two Fs, and 4sin30 that of a Y component. And the two X components are in opposite directions along the X axis.mcrooster said:
My bad. Fr should be 5.65.haruspex said:
##(4\cos(30))^2+(4\sin(30))^2=4^2\cos^2(30)+4^2\sin^2(30)=4^2(\cos^2(30)+\sin^2(30))=4^2##.mcrooster said:
Yes.mcrooster said:
That gives me a y force of -4kN. This does not give me the answer to Tb. Do I now use the Z and Y axis to figure out my answer since Fx = 0haruspex said:
Yes. As I indicated in post #2, it has reduced to being a 2D problem.mcrooster said:
To determine the equilibrium of a rigid body in 3D, you must first calculate the forces acting on the body. These forces include external forces, such as gravity or applied forces, and internal forces, such as tension or compression. Once all forces are identified, you can use the equations of equilibrium (sum of forces and sum of moments) to solve for the unknowns and determine if the body is in equilibrium.
Static equilibrium refers to a system that is at rest or moving at a constant velocity, with no acceleration. In this state, the sum of all forces and the sum of all moments acting on the system must be equal to zero. Dynamic equilibrium, on the other hand, refers to a system that is in motion with a constant acceleration. In this state, the sum of all forces and the sum of all moments acting on the system must be equal to the mass of the system multiplied by its acceleration.
To calculate the torque required to maintain equilibrium, you must first identify the pivot point or axis of rotation. Then, you can use the equation τ= r x F, where τ is the torque, r is the distance from the pivot point to the point of application of the force, and F is the magnitude of the force. This equation takes into account the direction of the force and the direction of rotation around the pivot point.
Yes, the center of mass can be used to determine equilibrium in 3D rigid bodies. The center of mass is the point where the body's mass is concentrated, and it can be used as the reference point for calculating the sum of moments. If the sum of moments around the center of mass is equal to zero, then the body is in equilibrium.
Some common examples of 3D equilibrium in everyday life include a book resting on a table, a ladder leaning against a wall, and a seesaw with equal weights on either side. In all of these examples, the forces acting on the objects are balanced, and there is no net torque, resulting in 3D equilibrium.