Cable tension problem

In summary: Then continue to solve for Fca.In summary, the problem involves finding the tension in cables ca and cb in a system in equilibrium, given a cylinder with a mass of 10 kg and an angle of 45 degrees. The equations and components needed for the solution are requested, along with a list of useful formulas for similar problems. The approach involves setting up force equations for horizontal and vertical components, and solving for Fca using basic algebra.
  • #1
markles
5
0

Homework Statement



hello i have a problem with this question.

the cylinder shown in fig1 has a mass of 10 kg. if theta = 45 and the system is in eqlibrium determain the tension in cables ca, cb.

Homework Equations



all i want is the equations and a guide to the i.e what each component is m=mass or g=gravity. and it would be really helpful is some provided outher useful formula for similar questions. as i have 3 or 4 and one includes a spring but i don't want to be cheeky and ask all 3 questions so if i got a list of formula i think i could apply them ok providedi know each component.


The Attempt at a Solution



10x9.81 = 98.1 and because the system is in equlibrium the total tension must equal 98.1.

Tca= 30=w1=10x 9.81
98.1/sin30 =196.2N

Tcb = Fca cos 45 = 196.2 cos 45 = 138.59N
these two answers are far to big i think and i don't know of any way to find the tension
 

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  • #2
Welcome to Physics Forums :smile:

markles said:

The Attempt at a Solution



10x9.81 = 98.1 and because the system is in equlibrium the total tension must equal 98.1.
Actually, no. That is only true for a mass hanging by a single, vertical cable.

Tca= 30=w1=10x 9.81
This makes no sense. In part, this equation says that 30=10x9.81?

98.1/sin30 =196.2N

Tcb = Fca cos 45 = 196.2 cos 45 = 138.59N
these two answers are far to big i think and i don't know of any way to find the tension

The approach, after drawing a free-body diagram, is to set up 2 separate force equations for the horizontal and vertical force components.
 
  • #3
if i were to do

+> Fcb cos 45 = Fca cos 30

+^ Fca sin 30 = Fcb sin 45 = 98.1N

then

Fcb = Fca cos 30/ cos 45

then sub Fcb with:

Fa sin 30+ Fca cos(30) x sin 45 / cos 45

Fca [sin 30 + (cos 30 x sin 45/cos 45)]

Fca=98.1

sub in Fca into Fcb = 9.81 x cos 30 / cos 45


Would that be the right kind of theory? If not i am lost thanks for you help and any futher is greatly appriciated.

Thank You
 
  • #4
markles said:
Fca [sin 30 + (cos 30 x sin 45/cos 45)]
Okay, that is the sum of the upward rope forces. If you set that whole expression equal to the downward 98.1 N force, you can then find Fca.

Fca=98.1
No.
 
  • #5
How would i do that? Could you give me the equation please?

Thank you
 
  • #6
Fca [sin 30 + (cos 30 x sin 45/cos 45)]

Fca=98.1

You have to modify this step.
Fca [sin 30 + (cos 30 x sin 45/cos 45)] = 98.1
Find Fca
 
  • #7
i don't know how to do that could you show me please?
 
  • #8
It's basic algebra. I would start by evaluating the expression,

(cos 30 x sin 45/cos 45)​
 

1. What is a cable tension problem?

A cable tension problem refers to a situation where the tension in a cable or wire is not balanced, causing it to either stretch or break. This can occur in a variety of systems, such as suspension bridges, cranes, or even simple household objects like clotheslines.

2. What causes a cable tension problem?

Cable tension problems can be caused by a variety of factors, such as unequal load distribution, faulty or worn-out cables, or external forces like wind or temperature changes. In some cases, human error or poor design can also contribute to cable tension problems.

3. How do you fix a cable tension problem?

The solution to a cable tension problem depends on the specific cause. In some cases, simply redistributing the load or replacing worn-out cables may solve the issue. Other times, more complex solutions such as reinforcement or redesigning the system may be necessary. It is important to consult with a professional engineer to determine the best course of action.

4. Can a cable tension problem be prevented?

While some cable tension problems may be unavoidable, others can be prevented through regular maintenance and inspections, proper installation and load distribution, and using high-quality materials. Implementing safety measures and following industry standards can also help prevent cable tension problems.

5. What are the potential consequences of a cable tension problem?

A cable tension problem can have serious consequences, depending on the system it occurs in. In some cases, it can cause structural damage or failure, leading to accidents and injuries. It can also result in downtime and costly repairs. Therefore, it is important to address cable tension problems promptly and effectively to avoid potential hazards.

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