Circular motion and parabolic orbit

[shrrikesh]

Homework Statement

A point object of mass m is connected to an inertialess string of length L, the other end of which is connected to a fixed point O. At time t=0, the object is assumed to move horizontally in a vertical plane from the bottom point A (OA=L). in the clockwise direction with an initial speed v₀ as seen in the figure.

http://img208.imageshack.us/img208/5223/figure.jpg

If $$\sqrt{2gL}$$<v₀<$$\sqrt{5gL}$$, then at a point B (the angle between OB and the horizontal direction is designated $$\theta$$) the magnitude of the force acting on the object from the string becomes zero, where OB=L and the velocity is perpendicular to OB. v being the magnitude of the vector velocity. If 0<$$\theta$$<$$\pi$$/2.

1) the speed v is given by...?

2) the initial speed is ...?

3) From the point B, for a while, the object takes a parabolic orbit till C where OC=L . The maximum elevation (with respect to location B) is expressed as ...?

4) In the case $$\theta$$=$$\pi$$/3, the angle $$\phi$$ measured as in fig. specifying the point C becomes. ...?

5) and finally the angle , the angle between the object velocity at the point C and the horizontal direction is ...?

Homework Equations

for no 1)

mv²/L-mgsin(90+$$\theta$$) = 0

for no 2)

decrease in Kinetic Energy = Gain in Potential Energy

for no 3)

H = v²sin²(90-$$\theta$$)/2g

I am not able to do for no 4 and 5.

The Attempt at a Solution

I've found out the answers for question 1,2 and 3 which are

$$\sqrt{gLsin\theta}$$, $$\sqrt{(2+3sin\theta)gL}$$ and v²cos²$$\theta$$/2g respectively.

I don't have any ideas to solve the last two ones.

 

[Gyro]

Hi!

https://www.physicsforums.com/showthread.php?t=324188