How Do You Calculate Tension in Wires Holding a Revolving Ball?

[ilovejesus]

Homework Statement

Two wires are tied to the 150 g ball shown in the figure. The ball revolves in a horizontal circle at a constant speed of 5.0m/s. gravity is 10m/s2.

Draw a free-body diagram and specify any relevant dimensions or angles.

Write expressions applying Newton's second law on the ball.

Calculate the tension in each of the wires.

If we remove the lower wire, but want the ball to revolve in the same path, what must we do to the ball. (i.e. increase decrease speed). Explain

[REALLY NEED HELP ON THIS]

 

[HallsofIvy]

Have you read the board rules? You are expected to attempt the problem yourself and SHOW what you have tried to do.

 

[ilovejesus]

Oh, sorry. I'm in a rush and I actually didn't read it. I attempted to make a freebody diagram, but all I came up with was that the two tensions added up equaled to the force of gravity. I don't think that is right though. I feel like there is supposed to be some sort of centripital force involved, but I don't know where

 

[Redbelly98]

Oh, sorry. I'm in a rush and I actually didn't read it. I attempted to make a freebody diagram, but all I came up with was that the two tensions added up equaled to the force of gravity. I don't think that is right though.

It's not. All three forces, added up using vector addition, equal m·a. And, it's helpful to separate the forces into x and y components to do the vector addition.

I feel like there is supposed to be some sort of centripital force involved, but I don't know where

m·a is the centripetal force; it does not get included in the freebody diagram. The freebody diagram should only have forces with identifiable, physical causes -- for example, gravity, rope/string tension, forces applied by people or other objects, friction, normal force, etc. The centripetal force is simply the net result of those forces.

 

[asteriatic]

I would approach this problem by first drawing a free-body diagram of the ball, showing all the forces acting on it. In this case, there are two tension forces, one from each wire, and the force of gravity acting downwards. The relevant dimensions would include the length of the wires and the angle at which they are attached to the ball.

To apply Newton's second law, we can write the equation Fnet = ma, where Fnet is the net force on the ball, m is the mass of the ball, and a is the acceleration of the ball. In this case, since the ball is moving in a horizontal circle at a constant speed, the acceleration is directed towards the center of the circle and has a magnitude of v^2/r, where v is the speed and r is the radius of the circle.

To calculate the tension in each wire, we can use the equation T = mv^2/r, where T is the tension, m is the mass of the ball, v is the speed, and r is the radius of the circle. Plugging in the given values, we can find the tension in each wire to be 3.75 N.

If we remove the lower wire, the ball will no longer have a horizontal force acting on it, causing it to move in a straight line instead of a circle. To keep the ball moving in the same path, we would need to increase the speed of the ball. This is because the centripetal force required to keep the ball in a circular motion is proportional to the square of the speed. So by increasing the speed, we can compensate for the loss of the horizontal force from the lower wire and keep the ball moving in the same path.