• Support PF! Buy your school textbooks, materials and every day products Here!

Maximum tension

  • Thread starter Ry122
  • Start date
565
2
http://users.on.net/~rohanlal/Q5.jpg [Broken]
The maximum force of the block, T, must be determined. The 2nd rope that the pulley is attached to has the same maximum tension force as the rope of the pulley which is 10kN.
Theta also needs to be determined.
 
Last edited by a moderator:

Answers and Replies

Dick
Science Advisor
Homework Helper
26,258
618
Could you possibly write the sum of all the forces on the pulley and set it equal to zero? There are two unknown tensions in the problem, T and the unnamed tension between the pulley and the support point. Balancing the forces should give you two equations in two unknowns.
 
565
2
is this what you mean?
make T = 10 since it will undergo the highest tension.
change in y = 10cos0-w=0
how do i do the x component?
 
Dick
Science Advisor
Homework Helper
26,258
618
I'm not even completely sure what your original question means. I was hoping if you started solving it I could figure that out, but I guess I was wrong. Why T=10? y=10cos0-w=0 looks kind of like a force balance equation for the weight. Is that what it's supposed to be? How about balancing the forces on the pulley?
 
nrqed
Science Advisor
Homework Helper
Gold Member
3,540
181
I'm not even completely sure what your original question means.
The way I interpret it is the following: There are three unknowns (the two tensions and the angle) and the constraint that neither tension must be over 10 kN.

The approach I would suggest would be to first assume that the tension T is the maximum value, 10 kN. And then solve for the other tension and the angle theta. If the other tension is less than 10 KN then that's it, that's the final answer to the problem.
If the other tension is above 10 kN, one has to start all over again by setting that other tension equal to 10kN and finding T and theta.
 
Dick
Science Advisor
Homework Helper
26,258
618
The way I interpret it is the following: There are three unknowns (the two tensions and the angle) and the constraint that neither tension must be over 10 kN.

The approach I would suggest would be to first assume that the tension T is the maximum value, 10 kN. And then solve for the other tension and the angle theta. If the other tension is less than 10 KN then that's it, that's the final answer to the problem.
If the other tension is above 10 kN, one has to start all over again by setting that other tension equal to 10kN and finding T and theta.
Ah! That makes sense, thanks.
 
565
2
The way I interpret it is the following: There are three unknowns (the two tensions and the angle) and the constraint that neither tension must be over 10 kN.

The approach I would suggest would be to first assume that the tension T is the maximum value, 10 kN. And then solve for the other tension and the angle theta. If the other tension is less than 10 KN then that's it, that's the final answer to the problem.
If the other tension is above 10 kN, one has to start all over again by setting that other tension equal to 10kN and finding T and theta.
this is what I had in mind but i dont know how to solve for the other tension. Can you show me how to do that?
 
Dick
Science Advisor
Homework Helper
26,258
618
You have a direction (angle) and magnitude of each of the three forces acting on the pulley. Split each into x and y components. You'll need to use a trig function of the angles.
 
Last edited:
565
2
This is what I came up with
sum of y components = 10cos0 +Fw + bcos30
sum of x components = bsin30 + 10sin0
I cant solve it because there's 3 unknowns
 
Dick
Science Advisor
Homework Helper
26,258
618
Ok, I'm guessing you are using b as the unknown tension and the symbol '0' to represent 'theta' (that's not a very good choice - just write e.g. cos(theta)). If that's the case then you are missing some signs. For example, one of the x forces should be positive and the other negative. They are pointing in opposite directions. Not all of the y forces are pointing in the same direction either. As for the other unknown 'Fw', the tensions on the two sides of the pulley are equal. So Fw isn't unknown, it's the same as T. Now there are two unknowns, b and theta.
 
565
2
yes b = unknown tension
Assuming T and Fw are both negative forces then
-10cos(theta)-10+bcos30=0
bsin30-10sin(theta)=0
Is this correct?
The answer I got was 60 degrees.
 
Last edited:
Dick
Science Advisor
Homework Helper
26,258
618
Yes, the equations are correct. And, yes, I seem to get 60 degrees as well.
 
565
2
No matter what value I have for T the answer is always 60 degrees. Should this matter?
 
Dick
Science Advisor
Homework Helper
26,258
618
No, you finally wind up with an equation for theta in which the T cancels out. This is a good thing. Is b>10kN? If so you will have to resolve the problem with b=10kN and then figure out what T is. If everything varies in proportion, this will save you a lot of time.
 
565
2
Is there a way to solve for b without having to make theta the subject of the equation.
 
Dick
Science Advisor
Homework Helper
26,258
618
Is there a way to solve for b without having to make theta the subject of the equation.
Solve one equation for sin(theta) and the other for cos(theta). Square and add them. sin(theta)^2+cos(theta)^2=1. Poof, no more theta.
 
565
2
-10cos(theta)-10+bcos30=0
bsin30-10sin(theta)=0

Im beginning to doubt that these equations are correct.
I think that either the -10 or the -10cos(theta) shouldn't be in there because they are the same force. Pulleys just change the direction of the force.
Does anyone agree with me?
 
Dick
Science Advisor
Homework Helper
26,258
618
Does anyone agree with me?
I don't. Those two terms are vertical components of two 10kN forces pointing in different directions. You were almost done with this problem. What's bothering you?
 

Related Threads for: Maximum tension

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
10K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
4K
Replies
3
Views
946
  • Last Post
Replies
3
Views
4K
Top