How Do You Calculate the Tension in a Cable Supporting a Collar on a Smooth Bar?

In summary, the problem involves finding the distance s between point C and an unknown point A, where s is the distance at which the tension in cable AB is 150N. The locations of points B, C, and D are given, but the location of point A is unknown. The solution involves equating the x, y, and z components of the forces acting on the collar A, considering the weight of the collar, and using trigonometric functions to find the angle between the tension in AB and the rod CD. The final solution is s = 0.305m.
  • #1
snowrock
2
0

Homework Statement



The cable AB keeps the 8-kg collar A in place on the smooth bar CD. The y-axis points upward. Determine the distance s from C to the collar A for which the tension in the cable is 150N.
location of:
B: (0m, 0.5m, 0.15m)
C: (0.4m, 0.3m, 0m)
D: (0.2m, 0m, 0.25m)

collar A's location is unknown. The required is the distance between C and collar A. The answer is 0.305m, but I need the solution for it.
For an easier look, http://img86.imageshack.us/img86/4710/392ij8.jpg"

Someone answered this in yahoo answers. Can someone verify it?
http://answers.yahoo.com/question/index;_ylt=AgV3Ti6P9WnWMOA1BU8rsIDzy6IX?qid=20061225063557AANnWr1"

Homework Equations



e dc= dc/|dc|
W=mg
edc=eac
s=distance between A and C

The Attempt at a Solution



DC=0.2i+0.3j-0.25k
e dc=0.4558i-0.6838j+0.5698k
I'm not sure about this part...
eab= -Axi+(0.5-Ay)j+(0.15-Az)k
sqrt(Ax^2+Ay^2+Az^2-Ay-0.3Az+0.2725)
eac= (0.4-Ax)i+(0.3-Ay)j-Azk
sqrt(Ax^2+Ay^2+Az^2-0.8Ax-0.6Ay+0.25)

sedci=-150eabi
sedcj=-150eabj
sedck=-150eabk

eabi=-Axi/|AB|
eabj=(0.5-Ay)j/|AB|
eabk=(0.15-Az)k/|AB|

I equated the "s" in the previous part and got...
Ay=0.5-1.5Ax
Az=1.25Ax+0.15
After that, my solutions just go in circles. I couldn't get what Ax is.
Also, Is my use of Ax, Ay, Az correct? I'm doubting about it.
 
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  • #2
The weight of the collar acts downward, but the movement of the collar is contrained by the rod between C&D, so one must find the force component along C&D, which acts toward D.

The tension in AB has a component which acts upward toward C.

For a static situation, the corresponding x, y, and z components of the forces must = 0.
 
  • #3


I can provide a general response to help guide you in solving this problem. First, it is important to understand the concept of unit vectors and their use in solving problems involving forces and distances. Unit vectors are used to represent the direction of a force or displacement, and they have a magnitude of 1. In this problem, the unit vector e_dc represents the direction of the cable pulling on the collar A.

To solve this problem, you will need to apply the principles of equilibrium, specifically the sum of forces and moments equaling zero. In this case, the sum of forces in the x, y, and z directions must equal zero, and the sum of moments around any point must also equal zero.

To start, you can use the given information to calculate the unit vector e_dc. Then, using the known location of point D and the unknown location of point A, you can calculate the distance between them (using the distance formula). Next, you can use the principle of moments to find the unknown distance s, by setting the sum of moments around point C equal to zero.

It is also important to carefully define your coordinate system and use consistent notation for the unknown distances and coordinates. In this case, you can define the x-axis as the direction from C to D, the y-axis as the vertical direction, and the z-axis as the direction perpendicular to the x-y plane. This will help you to keep track of your calculations and ensure that your final answer is accurate.

In summary, to solve this problem you will need to calculate the unit vector e_dc, use the distance formula to find the distance between points D and A, and then use the principle of moments to find the unknown distance s. I hope this helps guide you in solving this problem.
 

Related to How Do You Calculate the Tension in a Cable Supporting a Collar on a Smooth Bar?

1. What are unit vectors?

Unit vectors are vectors with a magnitude of 1 and are used to indicate direction in a coordinate system. They are typically represented by i, j, and k in 3-dimensional space.

2. How do I find the unit vector of a given vector?

To find the unit vector of a given vector, divide the vector by its magnitude. This will result in a vector with a magnitude of 1 and the same direction as the original vector.

3. What is the importance of unit vectors in physics?

In physics, unit vectors are used to represent the direction of a physical quantity. They are essential in calculating forces, velocities, and accelerations in different directions.

4. Can unit vectors be negative?

No, unit vectors cannot be negative. They are always positive and have a magnitude of 1, indicating direction without any change in magnitude.

5. How are unit vectors used in vector addition and subtraction?

In vector addition and subtraction, unit vectors are used to break down a vector into its components in different directions. This makes it easier to perform calculations and determine the resultant vector.

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