Tension in two strings and different angles

In summary, the conversation discusses a problem involving a police officer suspended by two cables and the use of equations to find the tensions in the cables. The participants suggest drawing a force diagram and separating the forces into horizontal and vertical components. Ultimately, a system of equations is used to solve for the two unknown tensions.
  • #1
Todd88
22
0

Homework Statement


In a rescue, the 72.0 police officer is suspended by two cables, as shown in the figure below.

image5.44.jpg



Homework Equations


T = mgsin(48)?
T2 = mgsin(35)?


The Attempt at a Solution


I used the above equations and it is not right. Me and my friend have been working on this for a while now and it's starting to get frustrating! Any help is appreciated!
 
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  • #2
You need to make a force (free body) diagram for the man. He has two tension forces pulling in the direction of those ropes and there is another force on him that you undoubtedly already know.

Separate each of the 3 forces into their horizontal and vertical components.
Then write that the sum of the horizontal forces is zero and the sum of the vertical forces is zero (because there is no acceleration in either direction). You should be able to solve the system of 2 equations for the two unknown tensions.
 
  • #3
Okay so Fg = 705.6 which means the normal force would have to be 705.6?

Since we know that, the y components of both angled strings are 705.6 but the x components are different?

Correct me if I'm wrong...
 
  • #4
Yes, Fg looks good. But there is no "normal" force. A normal force presses two objects together as in a block on a ramp.

So you have Fg down and you have T1*sin(35) up and also T2*sin(48) up.
You get this by drawing the T1 force vector at its angle, then drawing a horizontal plus a vertical arrow that ends in the same place. Use trig to find their lengths. Finally, forget the T1 and think only of the horizontal and vertical forces instead.

Sum those and set the total equal to zero.

Then do the horizontal forces.
 
  • #5
T1 and T2 would be different values correct? So I would have to do a system of equations first solving for either T1 or T2 and then plug those in?
 
  • #6
Yes.
 
  • #7
Wait you edited your answer and now it's confusing.

For the y components, wouldn't it just be 705.6? The x components would be different for both angles but how would they even out to 0?
 
  • #8
It is true that the two vertical tension components add up to mg (705.6).
That gives you one equation relating T1 and T2 (with two sines in it, of course).
You need another equation so you can solve a system of 2 equations to find the 2 unknowns. That other equation is
Sum of horizontal forces = 0.
 

1. What is tension in two strings?

Tension in two strings refers to the pulling force that is exerted on each string in opposite directions. It is the force that keeps the strings taut and prevents them from collapsing or becoming slack.

2. How is tension affected by different angles?

The tension in two strings is affected by the angle at which they are pulled. The greater the angle, the higher the tension in the strings. This is because a larger angle results in a greater horizontal component of the force, which adds to the tension in the strings.

3. What happens to the tension if one string is pulled at a steeper angle than the other?

If one string is pulled at a steeper angle than the other, the tension in that string will be greater. This is because the angle affects the horizontal component of the force, and the string with the steeper angle will have a larger horizontal component, resulting in higher tension.

4. Does the length of the strings affect the tension?

Yes, the length of the strings can affect the tension. A longer string will have a greater tension than a shorter string, given the same force and angle. This is because longer strings have more surface area and therefore, more resistance to the force applied.

5. How does the weight of the objects attached to the strings impact the tension?

The weight of the objects attached to the strings has a direct impact on the tension. The heavier the objects, the higher the tension in the strings. This is because the weight of the objects adds to the force being applied to the strings, increasing the overall tension.

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