How to Calculate the Z Force of a Static Object in a 3D Force System?

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In summary, the problem involves a bob attached to three pulleys at different heights with masses to achieve a theoretical equilibrium. The equations used include Newton's law of gravitation and trigonometry to calculate the forces in each string, with the final result being a Z force of -.83N in string A.
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Homework Statement


A Bob is centered on a force plate attatched to three pulleys of different heights by string. these pulleys are located at 360*, 270* and 140* on the plate with masses to make the bob centered of .075kg, .054, and .080 respectively. The measured angles for each string were 46.4*, 41.5*, and 35.6* The object is to see how close to a theoretical 0 net force equilibrium we can get. The Bob weighs .1375kg.


Homework Equations


string A: .075*9.8=.74N, angle was measured to be arctanΔ6.3/Δ6=46.4*. Then for the horizontal force I have X=.74sin46.4=.54N. Y=.74sin46.4=.51 and I am unsure how to get the Z force. This is where I am stuck. I have completed the previous equations for all 3 strings and for the x and Y vectors by using FTx=ƩFx-Fbob=1.54-1.34=.2, Fty=ƩFy-Fbob=0. I am really stuck. Any help would be appreciated. Thanks.
 
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The Attempt at a SolutionFor the Z force of string A, we can use the equation Ftz=ƩFz-Fbob. Then we need to determine Fbob. Fbob can be determined using Newton's law of gravitation. Fbob=m*g, where m is the mass of the bob and g is the acceleration due to gravity. Therefore, Fbob=.1375*9.8=1.34N. Now, we can calculate Ftz=ƩFz-Fbob. To determine ƩFz, we can use trigonometry to calculate the vertical component of the force. ƩFz=.74*sin46.4=.51N. Therefore, Ftz=.51-1.34=-.83N. Therefore, the Z force of string A is -.83N.
 

FAQ: How to Calculate the Z Force of a Static Object in a 3D Force System?

What is the concept of 3D sum of forces?

The concept of 3D sum of forces refers to the mathematical calculation of the net force acting on an object in three-dimensional space. It takes into account all the forces acting on an object, including their magnitude, direction, and point of application, to determine the overall effect on the object's motion.

How is the 3D sum of forces calculated?

The 3D sum of forces is calculated by breaking down all the forces acting on an object into their respective components in the x, y, and z directions. These components are then added together using vector addition to determine the net force in each direction. The magnitude and direction of the resulting net force represent the 3D sum of forces acting on the object.

What is the difference between 3D sum of forces and 2D sum of forces?

The main difference between 3D sum of forces and 2D sum of forces is the number of dimensions in which the forces are acting. 2D sum of forces only considers forces in the x and y directions, while 3D sum of forces takes into account forces in the x, y, and z directions. This allows for a more accurate representation of the forces acting on an object in three-dimensional space.

What is the significance of 3D sum of forces in static objects?

In static objects, the 3D sum of forces is equal to zero. This means that all the forces acting on the object are balanced, and there is no net force causing the object to move. This concept is crucial in understanding the stability and equilibrium of static objects, as any imbalance in forces would result in the object's motion.

How is the 3D sum of forces used in real-world applications?

The 3D sum of forces is used extensively in engineering and physics to analyze and predict the behavior of objects in three-dimensional space. It is used to design stable structures, determine the strength of materials, and calculate the forces acting on moving objects. It also has practical applications in fields such as architecture, biomechanics, and aerospace engineering.

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