Statics- equilibrium of rigid bodies

In summary, the conversation discusses a problem involving a 1x1.2m sheet of plywood that is hinged at two points and is supported by a small block. The problem asks to determine the vertical component of the reaction at three different points. The approach to solving the problem involves creating a free body diagram and taking moments about an axis.
  • #1
Litcyb
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Homework Statement



An opening in a floor is covered by a 1×1.2-m sheet of plywood of mass 18 kg. The sheet is hinged at A and B and is maintained in a position slightly above the floor by a small block C. Determine the vertical component of the reaction (a) at A, (b) at B, (c) at C.

Homework Equations


The Attempt at a Solution



I know how to approach this problem, however, I am just a bit confused on how to set up my F.B.D. i attached the correct f.b.d for this problem . My question is, how come if we take the moment about point A, we only have a reaction force in the j direction at support B?
 

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  • #2
The plywood is hinged at A and B and the only loads imposed are the weight and the reaction due to the block at C. All of these forces are in the direction of the y-axis. It doesn't matter about which point you take moments, it's just the nature of the forces for this particular problem.
 
  • #3
You take moments about an axis, not a point. That is the key to solving 3-dimensional problems like this.
 

Related to Statics- equilibrium of rigid bodies

1. What is statics and why is it important?

Statics is a branch of mechanics that deals with the study of forces acting on a stationary object. It is important because it helps us understand the behavior of structures and machines under various forces, and allows us to design and build stable and safe structures.

2. What is the difference between statics and dynamics?

The main difference between statics and dynamics is that statics deals with stationary objects while dynamics deals with moving objects. Statics focuses on the equilibrium of forces acting on an object, while dynamics takes into account the acceleration and motion of an object under the influence of forces.

3. How do you determine if a rigid body is in equilibrium?

A rigid body is in equilibrium when the sum of all the external forces acting on it is equal to zero and the sum of all the external torques (rotational forces) is also equal to zero. This means that the body is not moving or rotating.

4. What is the principle of moments in statics?

The principle of moments states that for a rigid body in equilibrium, the sum of the clockwise moments (torques) about any point must be equal to the sum of the counterclockwise moments about the same point. This principle is used to solve problems involving forces and torques acting on a rigid body.

5. How do you calculate the center of gravity of a rigid body?

The center of gravity of a rigid body is the point where the entire weight of the body can be considered to act upon. It can be calculated by finding the weighted average of the positions of all the particles in the body. Alternatively, it can also be found by suspending the body at different points and finding the point where it balances perfectly.

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