How Do Tensions in Upper and Lower Strings Differ in Uniform Circular Motion?

In summary: Therefore, for the x direction, you have T1sin@ - T2sin@ = ma and for the y direction you have T1cos@ + T2cos@ - Mg = 0. Solving these simultaneous equations will give you the tensions in the two strings.In summary, The tension in the two strings, T1 and T2, will not necessarily be equal. To find the tensions, you need to consider the forces acting on the ball, which are the tensions of the two strings and its weight. Setting up equations for the x and y directions and solving them will give you the tensions in the two strings.
  • #1
student 1
76
0

Homework Statement


A 4.00 kg object is attached to a vertical rod by two strings. The object rotates in a horizontal circle at constant speed 6.00m/s. Find the tension in the upper string and the lower string.
View attachment phy2.bmp

Homework Equations


C=2[tex]\pi[/tex]r
T=(M)V^2)/r


3. The Attempt at a Solution [
The tension should be easy. Since you have the speed and r. and the mass. Will the tension be the same for both strings though?
 
Physics news on Phys.org
  • #2
student 1 said:

Homework Statement


A 4.00 kg object is attached to a vertical rod by two strings. The object rotates in a horizontal circle at constant speed 6.00m/s. Find the tension in the upper string and the lower string.
View attachment 14466

Homework Equations


C=2[tex]\pi[/tex]r
T=(M)V^2)/r


3. The Attempt at a Solution [
The tension should be easy. Since you have the speed and r. and the mass. Will the tension be the same for both strings though?

Although I can't see your attachment I can say that the tension in the two strings, will not, in general be equal. I hope the attachment is a FBD, if it isn't, I suggest that you draw one.
 
  • #3
Anyone help me?? I know the top string has force of Tcos@-Mg in the y direction and Tsin@ in the x direction. I need help on the bottom string would it be pulling the ball down as well so you would have T+MG for y direction and x direction would be TSin@?
 
  • #4
student 1 said:
Anyone help me?? I know the top string has force of Tcos@-Mg in the y direction and Tsin@ in the x direction.
Good :approve:
student 1 said:
I need help on the bottom string would it be pulling the ball down as well so you would have T+MG for y direction and x direction would be TSin@?
You need to be careful here. Firstly with the direction, for the top string you have taken up as positive (i.e. the ball's weight is negative), however for the bottom string you have taken down to be positive (i.e. the ball's weight and the tension in the bottom string is positive). You need to chose one convention and stick to it throughout.

Secondly, as I said previously, the tensions in the two strings needn't be equal. Therefore, you need to use different symbols for the tension in the upper and lower string, perhaps T1 and T2, as opposed to simply T.

In addition, instead of considering the string separately, you should consider the forces acting on the ball, which are the tensions of the two strings and it's weight.
 

Related to How Do Tensions in Upper and Lower Strings Differ in Uniform Circular Motion?

What is uniform circular motion?

Uniform circular motion is the motion of an object along a circular path at a constant speed. This means that the object covers equal distances in equal amounts of time, resulting in a circular shape.

What is the difference between uniform circular motion and non-uniform circular motion?

Uniform circular motion maintains a constant speed throughout the circular path, while non-uniform circular motion involves changes in speed or direction along the circular path.

What is centripetal force in uniform circular motion?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary to maintain the circular motion.

How is uniform circular motion related to Newton's Laws of Motion?

Uniform circular motion is related to Newton's first law, which states that an object in motion will remain in motion in a straight line at a constant speed unless acted upon by an external force. In uniform circular motion, the centripetal force acts as the external force to keep the object moving in a circular path.

What are some real-life examples of uniform circular motion?

Some examples of uniform circular motion include the motion of planets around the sun, the motion of a car around a curved track, and the motion of a Ferris wheel. Essentially, any object that moves in a circular path at a constant speed can be considered an example of uniform circular motion.

Similar threads

  • Introductory Physics Homework Help
2
Replies
55
Views
831
  • Introductory Physics Homework Help
Replies
8
Views
212
  • Introductory Physics Homework Help
Replies
19
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
2K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
7K
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top