Tension. Application of Newton's Laws.

In summary, the tension in Cable A is 150 N. For Cable B and C, the total tension is 256 N, but since the load is shared equally between the two cables, the tension in each cable is 128 N. Utilizing the geometry of the problem and using trigonometry, the tension in Cable B and C can be found.
  • #1
valeriex0x
43
0

Homework Statement



Two weights are hanging by the following cables, A, B, C.
1. Find the tension in Cable A.
2. Find the tension in Cables B and C.

-----ceiling----------
\ 60) (60 /
\ /
\ /
B \ / C
\ /
\ /
[_] small box:72 N
|
A |
~~~
| | Big Box: 150 N
~~~

Homework Equations



Free body diagram of big box, maybe some trig for finding cables b or c


The Attempt at a Solution



1.
I know that the big box has a Force:weight pointing down of 150 N, and normally, if it was resting on a flat surface it would have normal force pointing up 150N. But because it is suspended by cable A from small box 72N, I'm not sure how to approach finding the tension in cable A. Would it be okay to think the tension in cable A is 150 N + 72 N?

2.
I am thinking I could draw a resultant? and that its magnitude would be 72 N, given by the box hanging from it. and from there do Opp/hyp or Sin (60).
-----ceiling----------
\ 60) | (60 /
\ | /
\ | /
B \ | / C
\ | /
\ |/
[_]



Any help would be appreciated! thanks

 
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  • #2
The figure is supposed to be an a triangle with its base parallel with the ceiling and its other two sides pointing into a V .
 
  • #3
For cable A try thinking of the small box as a "ceiling" with only cable A below it and from that cable, the large box would be hanging. What would you say the tension is in that situation? Is this situation any different?

For part (b) don't forget that you need to include both the small box's weight (force) AND the large box's weight (force).
 
  • #4
1. So to find the tension in Cable A, I take the 72 N pointing down, and the 150 N pointing up, and get a net force of 78 N. Would that be correct. I feel confused into thinking that the sum of forces should be zero if these boxes are hanging in equilibrium.?

2. 72 N + 150 N= 222N(sin(60))= 192 N the tension in cable B!>??
 
  • #5
valeriex0x said:
1. So to find the tension in Cable A, I take the 72 N pointing down, and the 150 N pointing up, and get a net force of 78 N. Would that be correct. I feel confused into thinking that the sum of forces should be zero if these boxes are hanging in equilibrium.?

2. 72 N + 150 N= 222N(sin(60))= 192 N the tension in cable B!>??

I guess I wasn't clear enough. For part (a), nothing is moving. Because nothing is moving, the only "force" being applied on the lower string is that of the large box. It is the same as if the large box were hanging from the ceiling from cable A and you were asked what the tension is in that cable.

For part 2, don't forget that you have 2 cables. Would cable B be taking all the load? Think of what you can do to take advantage of the geometry in the problem.
 
  • #6
1. The tension in Cable A is 150 N.
2. The tension in Cable B=Cable C = 128 N.

2) 72 N + 150 N= 222 N
Sin(60)= opp/hyp=222N/x=.8660254
Put sin(60) over one, cross multiply, solve for x (Cable B) x= 256 N

but that is the total tension.

Total Tension 256N divide by 2 = 128N tension in cable b and c

??! I think i got it!
 

What is tension?

Tension is a force that is transmitted through a string, rope, cable, or any other type of material that is under stress. It is a pulling force that results from the interaction between two objects.

How is tension related to Newton's laws?

Tension is related to Newton's laws in that it is a result of the application of Newton's third law, which states that every action has an equal and opposite reaction. In the case of tension, the force applied by one object is countered by an equal and opposite force applied by the other object.

Can tension ever be greater than the applied force?

No, tension can never be greater than the applied force. This is because of Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on the object. As tension is a result of a reaction force, it can never be greater than the original applied force.

What is the relationship between tension and the angle of the string?

The relationship between tension and the angle of the string is that tension increases as the angle of the string increases. This is because as the angle of the string increases, the vertical component of the force acting on the object also increases, resulting in a larger tension force.

How is tension calculated?

Tension is calculated using the formula T = mg + ma, where T is tension, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object. This formula takes into account the force of gravity and the acceleration of the object in determining the tension force.

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