A Box is suspended by two strings, what is the tension?

  • #1
1. The problem statement, all variables, and given/known data
Suppose a block is suspended by two strings, one, T1, is anchored at 30 degrees to the horizon, the other, T2, at 60 degrees to the horizon. If the block weighs 100 kg, what is the tension in the two strings?
Assume that:
The 30-degree angle is Phi.
The 60-degree angle is Theta.
M = 100 kg
g = 10 m/s^s

Homework Equations


(I had to create them myself, so they will be shown in the attempt section.)

The Attempt at a Solution


This image details my attempt. I am fairly certain that I got the correct answers, but I would really appreciate confirmation as well as an explanation for why certain things may be sin or cos. Most of the formulas are ones the professor just gave to us in class, and instead of expecting us to know how to create them, he just wants us to memorize them, which I struggle with unless I know the basis behind it.

7Sx1bqD.jpg
 

Answers and Replies

  • #2
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
13,668
6,168
The key equation that you have is:

##T_1 = \frac{mg}{\tan(\theta) \cos(\phi) + \sin(\theta)}##

Which is very good!

In fact, if you then calculate a similar expression for ##T_2## you will see the symmetry of the solution.
 
  • #3
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
9,103
2,493
To add to PeroK's answer, a useful thing to memorize is that if angles θ and φ are complementary, i.e. θ + φ = 90o, the sine of one is the cosine of the other. If you use this fact to express T1 in terms of one of the angles, say θ, your expression will simplify to a great extent. Do the same for T2 and you should recognize the expression relating the two tensions to the weight as something old and familiar.
 

Related Threads on A Box is suspended by two strings, what is the tension?

Replies
1
Views
2K
Replies
23
Views
3K
Replies
10
Views
161
  • Last Post
Replies
16
Views
2K
Replies
2
Views
33K
Replies
4
Views
15K
Replies
3
Views
2K
Replies
11
Views
878
Top