Problem 37P

Two wires are tied to the 2.0 kg sphere shown in FIGURE. The sphere revolves in a horizontal circle at constant speed.

a. For what speed is the tension the same in both wires?

b. What is the tension?

FIGURE

Solution 37 P:

Step 1 of 2:-

a)

Here we have to find the speed of rotation.

The pictorial representation is given below.

Now, let’s break the problem componentwise.

For x direction,

---------------------(1)

For y direction,

--------------------(2)

Let’s calculate and .

Both are equal to 1.36.

As, the two tensions and must be same as per our demand, we can equate equation (1) and (2).

-----------------(3)

The isoscale property of the triangle states that,

So,

.

So, the velocity will be 2.91 m/s.