How Do You Calculate Tension in a Swinging Object?

[AryRezvani]

Homework Statement

One end of a cord is fixed and a small 0.310-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.50 m as shown in the figure below. When θ = 28.0°, the speed of the object is 9.00 m/s. At this instant, find each of the following.

(a) the tension in the string

(b) the tangential and radial components of acceleration

(c) the total acceleration

Homework Equations

Hmm seems like you'd need a grasp of your basic trigonometry, and Newton's second law: ƩF = mg

The Attempt at a Solution

Okay, well let's start with the tension.

Tension is the force acting on the rope. And... acting downward is the force of gravity, right? So would we begin by representing the dashed line as part of a triangle where the string is the hypotenuse. Then we'd use SohCahToa and set up the following equation:

Sin (28.0) = (.310)(9.8)/T

And then proceed to solve.

 

[CWatters]

Hint: Regarding the tension.. Is it just the force of gravity?

 

[Cbray]

You can easily find the Tension a different way.
Ask yourself, What is Centripetal force?
My very brief answer: A tangential force to somethings motion needed to make that something move in a perfect circle.
Oi! That seems like our situation! The ball is traveling in a circle (until the string comes into contact with the block above, most likely a roof of some sort) so we can use the centripetal force equation! (Please learn how to derive this, if you don't you're just another person looking for the first letter of the alphabet on a piece of paper, which is really pathetic).
T_string = m*v^2/r
Plug and chug my friend.
For the rest of the questions it seems pretty intuitive.

 

[AryRezvani]

You can easily find the Tension a different way.
Ask yourself, What is Centripetal force?
My very brief answer: A tangential force to somethings motion needed to make that something move in a perfect circle.
Oi! That seems like our situation! The ball is traveling in a circle (until the string comes into contact with the block above, most likely a roof of some sort) so we can use the centripetal force equation! (Please learn how to derive this, if you don't you're just another person looking for the first letter of the alphabet on a piece of paper, which is really pathetic).
T_string = m*v^2/r
Plug and chug my friend.
For the rest of the questions it seems pretty intuitive.

Hmm tried that one out and came out wrong

Hint: Regarding the tension.. Is it just the force of gravity?

The mass is acting down as well? lol

 

[AryRezvani]

Come on guys . i just need to know how to find the tension and I'm good to go on part b to the end!

from what I understand, the only forces acting upon the rope are those of the rope itself and gravity. i used mv^2/r + mg and I got around 13.4. my online homework keeps telling me I'm close!

 

[Cbray]

Come on guys . i just need to know how to find the tension and I'm good to go on part b to the end!

from what I understand, the only forces acting upon the rope are those of the rope itself and gravity. i used mv^2/r + mg and I got around 13.4. my online homework keeps telling me I'm close!

Yes, as I said, make sure you include the centripetal force needed to keep it moving in a circle. Now you need to find the other 'part' of the tension which is due to the gravitational pull of the Earth on the sphere (You have to specify that there is a gravitational force! I'm assuming you're on the Earth). Since it's not parallel to the string, there is going to be a parallel component force opposite to the direction of the spheres momentum (which will eventually slow the ball down and make it oscillate back and forth), will this effect the tension in the string? NO! The gravitational force parallel component is parallel to the balls momentum, but perpendicular to the string, therefore it doesn't effect the tension! So the only force that acts on the string is the perpendicular force of the gravitational force acting on the ball. So we just need to find this.
T_string = m*v^2/r + mgcosx
T_string ~ 7

Hopefully that answered your question.