Question About a 3D Equilibrium Problem

In summary, the conversation discusses finding the moment of a 50lb force about the x,y,z axes. The individual attempted to use a cross product to calculate the moment, but the answer key showed a different value for the moment about the x-axis. The conversation also mentions a torque on a shaft and using that to calculate the tension force in the y direction for a belt.
  • #1
lc99
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Homework Statement



upload_2018-3-26_23-4-41.png

Homework Equations

The Attempt at a Solution


rxF
I'm trying to find the moment of the 50lb about the x,y,z axes. So, i did the vector from the origin to the top of the larger wheel crossproduct with the force vector of 50.

Thus, Vector Origin to Wheel x F vector = (0.2i +0.15k) x (50cos45j + 50sin45k) = 7.07k -7.07j - 5.3i

However, in the answer key, the moment about the x-axis isn't 5.3 but 7.5? What did i do wrong?
 

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  • #2
The difference in belt tension on A, is a torque on the shaft.
That torque makes it possible to calculate T in Newton in the y direction.
What value do you get for the belt B tension force T ?
 

FAQ: Question About a 3D Equilibrium Problem

1. What is a 3D equilibrium problem?

A 3D equilibrium problem is a physical or mathematical problem that involves finding the state of balance or stability of a system in three dimensions. This means that forces acting on the system in all three directions (x, y, and z) are balanced, resulting in no overall movement or rotation.

2. How do you solve a 3D equilibrium problem?

To solve a 3D equilibrium problem, you need to first identify and draw a free body diagram of the system, which shows all the external forces acting on the system. Then, you can apply the equations of equilibrium, which state that the sum of all forces in each direction (x, y, and z) must equal zero, and the sum of all moments must also equal zero. These equations can be solved simultaneously to find the unknown forces and/or angles.

3. What are some common types of 3D equilibrium problems?

Some common types of 3D equilibrium problems include problems involving objects on inclined planes, trusses or bridges, and objects suspended by multiple ropes or cables. These problems can also involve different types of forces, such as tension, compression, and shear forces.

4. What are the key assumptions made in solving a 3D equilibrium problem?

The key assumptions made in solving a 3D equilibrium problem include assuming that the system is in static equilibrium (meaning it is not moving or rotating), that all forces are acting at a single point, and that the forces are acting at right angles to each other. Additionally, the problem may assume that the object is rigid and that there is no friction present.

5. How does solving a 3D equilibrium problem relate to real-world applications?

Solving 3D equilibrium problems is essential in many real-world applications, such as engineering, architecture, and physics. It allows us to analyze and design structures and systems to ensure they can withstand various forces and remain in a state of balance. For example, understanding 3D equilibrium is crucial in designing stable bridges, buildings, and other structures.

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