Help: A ball attached to two strings (circular mtoion)

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Homework Help Overview

The problem involves a ball of mass 1.21 kg attached to a rotating shaft by two strings, creating circular motion. The tension in the upper string is given as 35N, and the length of the strings is 1.6m. The tasks include drawing a free body diagram, determining the tension in the lower string, calculating the net force acting on the ball, and finding the speed of the ball.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the challenges of creating free body diagrams and breaking down forces into components. There is a focus on the vertical and horizontal components of tension and how they relate to the forces acting on the ball. Some participants question the assumptions about net forces in the vertical direction and the implications of uniform circular motion.

Discussion Status

Participants are actively exploring the relationships between the forces acting on the ball and the geometry of the setup. Some guidance has been provided regarding the use of tension components and the need for a diagram to clarify the situation. Multiple interpretations of the radius of rotation and the geometry involved are being discussed, indicating a productive exploration of the problem.

Contextual Notes

There is uncertainty regarding the angles formed by the strings and the implications for calculating the radius of the circular path. Participants are also considering the need for additional information, such as the angle between the strings, to fully resolve the problem.

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Homework Statement


A ball of mass 1.21 kg is attached to a rotating shaft by two strings, putting the ball into circular motion. Tension on the upper string is 35N. (The length of the strings is 1.6m)

a) draw a free body diagram for forces acting on the ball.
b) determine the tension in the lower string
c) determine the net force acting on the ball
d) determine the speed of the ball


Homework Equations



ac= v^2/r

Fc=mac

The Attempt at a Solution




My problem is with a) I always have a hard time doing free body diagrams and breaking down the x and y components. Once I get that I know how to solve for c) and d). Some direction would be much appreciated!
 
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If the ball is moving in uniform circular motion, is there any net force in the vertical direction? Perhaps you can use this to your advantage.
 
yes i assumed that the fnet in the y direction is zero. but what about the two strings?
 
could someone please point me in the right direction as to find b)?
 
I assume the ball is traveling in a horizontal circle? A diagram would be helpful.

The strings apply their tension forces to the ball. Consider that the ball is centripetally accelerating and that the radial component of the net tension on the ball provides the centripetal force.
 
The sum of the vertical components of the tensions must equal mg to keep the ball suspended. The sum of the horizontal components must equal mv^2/r. But I don't see any way to actually get a number for anything unless you know the angle between the strings or the radius of rotation r.
 
I assume the radius of rotation would be 1.6m
 
Cate said:
I assume the radius of rotation would be 1.6m
Isn't that the length of the strings? (Total length? Or length of each?) Are the strings horizontal?
 
yes, 1.6 m is the length og the strings (individual) but it's also the disatnce between the two strings on the rod
 
  • #10
The diagram looks like #14 at this web page

http://teachers.oregon.k12.wi.us/fishwild/APPhysics/ForceMotion2.pdf
 
Last edited by a moderator:
  • #11
Cate said:
yes, 1.6 m is the length og the strings (individual) but it's also the disatnce between the two strings on the rod
Apply a little triangle geometry and you can figure out the radius of the ball's circular path.
 
  • #12
what do you mean trianle geometry? why isn't the radius 1.6m? how will this help me solve for the lower tension
 
  • #13
Cate said:
what do you mean trianle geometry? why isn't the radius 1.6m? how will this help me solve for the lower tension
If the string is 1.6m and it is at some angle with the horizontal, how can the radius also be 1.6m?

Draw yourself a diagram. The rod and the two strings form an equilateral triangle.
 
  • #14
o.k so if it's an equaliteral trangle then all three sides are 1.6m so I'm trying to find the height of the triangle?
 
  • #15
That's right. Or just make a right triangle by drawing in the radius. (What are the angles of an equilateral triangle?)
 
  • #16
I got the radius is about 1.39 m
 
  • #17
Cate said:
I got the radius is about 1.39 m
Looks good.
 
  • #18
thanks for your help, but could you give me a hint has to how to solve for the lower tension?
 
  • #19
What's the net horizontal force on the ball? (Call the lower tension T.) That force is the centripetal force.
 

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