Velocity and tension for 100g block swinging on 50cm wire

[Kernul]

Homework Statement

A block of 100g is attached to a wire inexstensible long 50cm. The block is left with a null initial velocity when the wire form an angle of 90° with the vertical. Calculate the velocity of the block and the tension of the wire when the block is at the position of equilibrium. Also calculate the velocity of the block when it forms an angle of 30° with the vertical after the position of equilibrium.

Homework Equations

The Attempt at a Solution

I started by calculating the velocity of the block at the position of equilibrium.
I used the law of conservation of mechanical energy and so:
K₀ = 1/2 * m * v₀² = 0
because the initial velocity is zero.
U₀ = 0
K = 1/2 * m * v²
U = - m * g * l
So we have
0 =1/2 * m * v² - m * g * l
v = sqrt(2 * g * l) = 3.13 m/s
After this I should calculate the tension of the wire too but I don't get how to do it.
I tried doing this:
{m * a_x = - T sin90° = - T
{m * a_y = T cos90° - P = - P = m * g
But beside this I don't know how to proceed.
Can someone help me how to do this little part?

 

[andrevdh]

Maybe by the sum of the forces acting on the block at the bottom needs to provide its centripetal acceleration?

 

[Kernul]

Maybe by the sum of the forces acting on the block at the bottom needs to provide its centripetal acceleration?

So you are telling me that the tension of the wire is T = m * a_c?
Because these way it would be a_c = v²/l = 19.6 m/s², so T = 0.1kg * 19.6 m/s² = 1.96 N
Is it correct?

 

[andrevdh]

The weight is also "contributing"

 

[Kernul]

So it is T = m * a_c - m * g = 0.98 N?

 

[andrevdh]

Draw a little diagram with the forces and maybe take positive as up (the direction of the acceleration)

 

[Kernul]

Draw a little diagram with the forces and maybe take positive as up (the direction of the acceleration)

I did it and the acceleration is positive so the counts are right, aren't they? I don't get why you asked me that.

 

[andrevdh]

The equilibrium position is at the bottom. I assumed you wanted to calculate the tension in the wire at this point in the swing.

 

[Kernul]

The equilibrium position is at the bottom. I assumed you wanted to calculate the tension in the wire at this point in the swing.

Yeah, that's the initial position. The right one is this:

 

[andrevdh]

Yes, so if you apply N2 and take up as positive then T - P = ma_c

 

[Kernul]

Oh! It's m * a_c = T - P, not T = m * a_c - P. I thought that the tension was directly the centripetal force minus the gravitational force and not that the centripetal force was the difference of the other two.
Thank you for your help!