Question

HELPPPP

Answer 1

@mathstudent55

Answer 2

@IhteshamMalik @HeroOfLove111

Answer 3

im not in this stuff yet srry again

Answer 4

@agent0smith

Answer 5

The first thing to understand is that as the ball spins around the pole, a centripetal force will create tension in the wires. That tension will have an x component and a y component (For reference the pole lies on the y-axis.)

Answer 6

Now the components of the forces along the y-axis will be:\[F _{g}=T _{cy1}+T _{cy2}\]Where Fg is the force of gravity; Tcy1 is the y-component of the tension in wire 1 (the lower wire); and Tcy2 is the y-component of the tension in wire 2 (upper wire). Expanding this equation in terms of components and angles we get:\[mg=Tsin \left( 30 \right)+Tsin \left( 60 \right)\]where m is the mass of the ball; g is the acceleration of gravity; and T is the tension in each wire. Note that the problem states that the tension in each wire is equal.

Answer 7

We can solve the above for T.

Answer 8

Now let's look at the forces in the x-direction:\[F _{c}=T _{x1}+T _{x2}\]where Fc is the centripetal force; Tx1 is the x-component of tension in wire 1; and Tx2 is x-component of tension in wire 2. Let's expand this:\[\frac{ mv _{t}^{2} }{ r }=Tcos \left( 30 \right)+Tcos \left( 60 \right)\]where vt is the tangential velocity of the ball; and r is the radius as measured from the pole to the ball. You can get T from above, and you know m and r. All that's left is to solve this last equation for vt, the variable the question is asking about.