Torque on a suspended plank

  • Thread starter tzar1990
  • Start date
  • #1
3
0

Homework Statement



The object is balance. Calculate T1 and T2. (yes, this plus the diagram is really the entirety of the question)

2stsFYi.png


Homework Equations



Στ = 0
τ = F⋅r
F = mg

The Attempt at a Solution



First, we treat the left side as a fixed point and solve for the vertical component of T2

Στ = 0
20⋅9.8⋅1 + 10⋅9.8⋅1.5 - 2T2y = 0
343 = 2T2y
T2y = 171.5

Next, we treat the right side as fixed and solve for the vertical component of of T1
Στ = 0
0.5⋅10⋅9.8 + 1⋅20⋅9.8 - 2⋅T1Y = 0
245 = 2T1Y
T1Y = 122.5

To verify, we check that the sum of the forces up should equal the sum of the forces down
T1Y + T2Y = 20*9.8 + 10 * 9.8
171.5 + 122.5 = 196 + 98
294 = 294

And this is the point where I get stuck. As far as I can tell, the situation is balanced for all cases where the force left due to T1 is equal to the force right due to T2, meaning you have everything from the case where both wires are vertical (and thus the x-components of their tension is zero) to the case where both are nearly horizontal (and the x-components of both approach infinity) being true.

What am I missing?
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,668
Unless you know the angles which T1 and T2 make with the horizontal, you can't work out the horizontal components of the tension.
Writing the moment equation can only give you the vertical component of the tensions.
 
  • #3
3
0
Thank you! That's what I told my student, but she seemed doubtful that an official question would have a misprint like that. Nice to hear that I'm not just missing something obvious.
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,582
5,982
Unless you know the angles which T1 and T2 make with the horizontal, you can't work out the horizontal components of the tension.
... except that, knowing one angle would do.
 

Related Threads on Torque on a suspended plank

  • Last Post
Replies
4
Views
20K
  • Last Post
Replies
4
Views
3K
Replies
7
Views
1K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
11
Views
9K
Replies
22
Views
784
  • Last Post
Replies
4
Views
11K
  • Last Post
Replies
1
Views
3K
Replies
1
Views
3K
Replies
3
Views
4K
Top