Solving a Centripetal Force Problem with Tension and Velocity | Homework Help

[John H]

Homework Statement

I'm having a hard problem conceptualizing this. It states that an object with a certain Mass M is being spun in a vertical circle. The object attached to a rope, and the object moving in circular path with constant radius. It also give you the velocity of the object. It asks you to find the tension force when the object is sideways. like the diagram blow. Note velocity is constant, object has uniform circular motion.

[PLAIN]http://img543.imageshack.us/img543/5048/object.jpg

The actual numbers don't matter to me, the book solves the problem by simply stating that the centripetal force comes from the tension, ignoring gravity, which correct, since gravity provides no force in this case along the radius. Here is where the book absolutely makes no sense, it obtains a tension by using the Fc = mv^2/r. Which is correct, but shouldn't this only be the tension in the x-component. Because a y-component of tension is required to to hold the object.

Thanks in advance.

Homework Equations

The Attempt at a Solution

Now my theory is that the object has enough velocity, so that it can mover vertically upwards after coming downwards that the tension force required in y-component is negligible.

 

[PhanthomJay]

No, the error here is in your initiial premise that the mass is moving with constant velocity in uniform circular motion. If there is a net force of gravity acting downward, what does this imply?

 

[John H]

Sorry, I should have stated constant speed. Still I can't see how that would solve the problem.

 

[PhanthomJay]

Sorry, I should have stated constant speed. Still I can't see how that would solve the problem.

It is not moving at constant velocity. Neither is it moving at constant speed. A particle moving in a vertical circle does not move at constant speed or constant velocity unless there is some external non conservative force or torque acting on it that does work. Draw a free body diagram of the object in the position shown. Again, you should note that there is a vertical force in the downward y direction that is not balanced by any other force in the upward y direction. What does Newton 2 say about net forces acting on an object?

 

[rwisz]

I would first like to commend you for taking the time to fully understand and question the problem at hand. It is important to have a thorough understanding of concepts in order to properly solve problems and draw accurate conclusions.

In this case, the solution provided by the book is correct. The tension force in the rope is the only force acting on the object in the horizontal direction, and therefore it must be equal to the centripetal force. This can be seen from the fact that the object is moving in a circular path with constant velocity, meaning there is no acceleration in the horizontal direction. Therefore, the net force in the horizontal direction must be zero, and the only force present is the tension force.

As for the y-component of tension, while it is true that there is a component of tension acting in the vertical direction, it is balanced by the force of gravity. This is because the object is moving in a vertical circle with constant radius, meaning the centripetal force is always directed towards the center of the circle. In this case, the force of gravity acts as the centripetal force, and therefore there is no need for an additional y-component of tension to hold the object in place.

I hope this explanation helps clarify the solution provided by the book. Keep up the critical thinking and questioning in your studies, as it is an important aspect of scientific inquiry.