Is the Calculated Tension in the Upper String Correct for a Stationary Ball?

In summary: I mentioned that you could use Newton's 2nd law to find the tension. You could also use the fact that the tension is a result of weight and inertia. In summary, the ball swings out an angle of 2 theta and has zero tangential acceleration at its farthest point.
  • #1
Joza
139
0
I have a ball. It is attached to a wall by a horizontal string to the left. it is attached to the ceiling by another string at an angle theta from the vertical to the right.

The ball is not moving. So I worked out that the tension in the upper string is w/(cos theta) , where w is weight. Is this correct before I go on?
 
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  • #2
I think I understand your description, but I am not sure. Try to post a pic through photobucket.com or something.

And yes, the vertical component of T in the upper string is equal in magnitude to the weight of the ball.
 
  • #3
Im not exactly sure how to get a picture up. But basically, I need to find the ratio of the tension at this point, in the upper string, to when it swings out to its farthest position when the horizontal rope is cut.


I am having trouble working out the tensions at these 2 points in the upper string. Any pointers?
 
  • #4
Looks like you got the first one correct. For the second one, work out the angle... draw all the forces and work out the tension as you did before. It's probably easier than you think.
 
  • #5
Joza said:
The ball is not moving. So I worked out that the tension in the upper string is w/(cos theta) , where w is weight. Is this correct before I go on?
So far, so good.

How far does the ball swing out when the string is cut? Hint: What direction is the acceleration zero?
 
  • #6
Joza said:
Im not exactly sure how to get a picture up. But basically, I need to find the ratio of the tension at this point, in the upper string, to when it swings out to its farthest position when the horizontal rope is cut.


I am having trouble working out the tensions at these 2 points in the upper string. Any pointers?

Go to Photobucket.com and register for free. Take a picture, scan, or screenshot of the problem. Log into phototbucket and click browse and find the file you want to upload. After it uploads just cut and paste the image code into thread.

Try it sometime. It's easy and it helps us help you!

Casey
 
  • #7
Thanks Casey, I'll try it soon!


It swings out an angle of 2 theta...its acceleration is zero at the farthest point right?
 
  • #8
Joza said:
It swings out an angle of 2 theta...
What angle does it make with the vertical at its farthest point?
its acceleration is zero at the farthest point right?
No it isn't. That's the big difference from the first case. But the component of the acceleration is zero in one particular direction. What direction would that be?
 
  • #9
It makes an angle of theta with the vertical at its farthest point. And the same before string is cut, so it swings out 2 theta.


Well, it swings out in an arc, so that's circular motion. At it's farthest point, it would have zero tangential acceleration right, because their is no change in its speed. But, its acceleration would be radial, that is it would be pointing towards the point of rotation?
 
  • #10
Joza said:
It makes an angle of theta with the vertical at its farthest point. And the same before string is cut, so it swings out 2 theta.
Good.

Well, it swings out in an arc, so that's circular motion. At it's farthest point, it would have zero tangential acceleration right, because their is no change in its speed. But, its acceleration would be radial, that is it would be pointing towards the point of rotation?
Actually, just the opposite! The tangential velocity is zero, but not the tangential acceleration. (The velocity is changing--it's only zero for an instant.)

As far as radial acceleration goes, how does that depend on tangential speed?
 
  • #11
Ah, yes yes, I see, silly me. It will have maximum acceleration back towards the wall at that instant will it?

Anyhow, I need the tension in the string at the 2 instants. I think I have the first one right - the tension is a component of the balls weight (ignoring the strings weight).

But it is this second instant that I am just having a little trouble with. My intuition tells me that the tension will be greater because the ball's inertia (correct?) :redface:

I need a numerical answer. So, I have the component of the balls weight, which is the same as before right? But shouldn't there be some other force?

I'm thinking it has something to do with its acceleration, but that isn't a force, it's the result of a force. Hmmm...
 
  • #12
Make use of the "hint" I tried to give you in post #8. Apply Newton's 2nd law along a direction where the acceleration is zero.
 
  • #13
I'm sorry guys, but I can't see my mistake.

I still get w/(cos theta) for both tensions...a points 1 and 2.

Where am I going wrong? In both situations, is the only force acting on the strings the weight of the ball (ie. string tension)?
 
  • #14
Joza said:
I still get w/(cos theta) for both tensions...a points 1 and 2.

Where am I going wrong? In both situations, is the only force acting on the strings the weight of the ball (ie. string tension)?
It's hard to say where you are going wrong, since you don't describe how you calculated the tension in the second case.

In the first case, there are three forces acting on the ball: its weight and the two string tensions. In this case the forces add to zero in all directions, since the ball is in equilibrium.

In the second case, only one string pulls on the ball. And the ball is not in equilibrium. (But its acceleration in one particular direction is surely zero. Find that direction and apply Newton's 2nd law.)
 
  • #15
Thanks for the input guys. I'm still having trouble with this one. Here is the picture:

http://i257.photobucket.com/albums/hh216/Megatallica/tension.jpg

I need to find the ratio of string in position B to position A. The horizontal string is cut and it swings out to B, max position.

I m confused. I calculated the tension in a as (mg)/(cos beta), that's mass of ball, string has no mass.
 
  • #16
Did you do what I suggested?
 
  • #17
Yes, but the problem is I can only identify once force acting on the string causing the tension...
 
  • #18
Only one force? I see three. The obvious one is the force of gravity- the weight of the ball- that's vertical, downward. The horizontal string is exerting a force horizontally, The string attached to the ceiling is at an angle- it has two components, one upward, the other horizontal.
 
  • #19
Just as before, all you need to consider are the forces on the ball. There are only two.

What about the acceleration? In which direction is it zero?
 

What is the "Tension in string problem"?

The "Tension in string problem" refers to a common physics problem that involves calculating the tension in a string or rope that is under a certain amount of stress or load. It is often used in engineering and other fields to determine the strength and stability of structures.

What factors affect tension in a string?

The tension in a string is affected by several factors, including the weight or load that is applied to it, the stiffness or elasticity of the string, and the angle at which the string is pulled. It is also influenced by external factors such as gravity and friction.

How do you calculate the tension in a string?

The tension in a string can be calculated using the formula T = F * cosθ, where T is the tension, F is the applied force, and θ is the angle at which the string is pulled. It is important to note that this formula only applies to ideal strings that are inextensible and have negligible mass.

What happens to tension in a string if the angle changes?

If the angle at which a string is pulled changes, the tension in the string will also change. As the angle increases, the tension will also increase, and as the angle decreases, the tension will decrease. This is because the force acting on the string is divided into two components, one parallel to the string (tension) and one perpendicular (normal force).

How does tension in a string affect the stability of structures?

The tension in a string is an important factor in determining the stability of structures such as bridges, cranes, and buildings. If the tension in a string exceeds its maximum limit, it can lead to failure and collapse of the structure. Therefore, it is crucial to accurately calculate and manage tension in strings in order to ensure the safety and stability of structures.

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