Calculating Tension on Two Wires Attached to 200g Sphere

[lmc489]

Two wires are tied to the 200 g sphere shown in figure. The sphere revolves in a horiIzontal circle at a constant speed of 7.80 m/s. The diagram shows a ball with two wires, each 1 m in length with a radius of .5 m

What is the tension in the upper wire?


What is the tension in the lower wire?

So, what i thought i would do was

T + mg = mv^2/r for the tension of the upper wire and

where T = 22.4

T - mg = mv^2/r for the tension of the lower wire..but after doing it i am not getting the right answers

and T = 26.3 but apparently neither are the right answers...

 

[LowlyPion]

Two wires are tied to the 200 sphere shown in figure. The sphere revolves in a horiIzontal circle at a constant speed of 7.80 . The diagram shows a ball with two wires, each 1 m in length with a radius of .5 m

What is the tension in the upper wire?What is the tension in the lower wire?

So, what i thought i would do was

T + mg = mv^2/r for the tension of the upper wire and

where T = 22.4

T - mg = mv^2/r for the tension of the lower wire..but after doing it i am not getting the right answers

and T = 26.3 but apparently neither are the right answers...

Have you properly accounted for the 30 degree angle the wires make with the vertical?

 

[baba89]

I would first make sure that all the given values are correct and that the equations used are appropriate for the situation. In this case, it seems that the equations used may not be applicable as they assume the sphere is in vertical motion, while in this scenario it is in horizontal motion.

To accurately calculate the tension on the two wires, we can use the centripetal force equation, Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the sphere, v is the speed, and r is the radius of the circle.

For the upper wire, the centripetal force is equal to the tension in the wire, so we can set Fc = T. Plugging in the given values, we get:

T = mv^2/r = (0.2 kg)(7.80 m/s)^2/(0.5 m) = 30.72 N

Therefore, the tension in the upper wire is 30.72 N.

For the lower wire, the centripetal force is equal to the sum of the tension and the weight of the sphere, so we can set Fc = T + mg. Plugging in the given values, we get:

T + mg = mv^2/r
T = mv^2/r - mg = (0.2 kg)(7.80 m/s)^2/(0.5 m) - (0.2 kg)(9.8 m/s^2) = 22.56 N

Therefore, the tension in the lower wire is 22.56 N.

It is important to note that the tensions in the two wires are not equal, as the upper wire is supporting the entire weight of the sphere while the lower wire is only supporting a portion of the weight. This can also be seen by the fact that the tension in the upper wire is greater than the tension in the lower wire.

In conclusion, to accurately calculate the tension on the two wires attached to the 200 g sphere, we need to use the centripetal force equation and take into account the weight of the sphere.