Determine the speed of the stone

[hyen84]

Need Help ASAP!

hey can some1 help me with these 2 physics questions..really need it...it's my last homework assigment and i have trouble with this 2...please help it's due tomorrow morning...show what me to do..thankssssssssss

1. A stone is tied to a string (length = 1.27 m) and whirled in a circle at the same constant speed in two different ways. First, the circle is horizontal and the string is nearly parallel to the ground. Next, the circle is vertical. In the vertical case the maximum tension in the string is 15% larger than the tension that exists when the circle is horizontal. Determine the speed of the stone.

2.Suppose the surface (radius = r) of a cylindrical space station is rotating at 33.8 m/s to provide artificial gravity. What must be the value of r for the astronauts to weigh 1/2 of their Earth weight?

 

[arildno]

1) In the horizontal circular motion case, only the string's tension can provide the required centripetal acceleration.
What forces can provide centripetal acceleration when the circular motion is vertical; in particular, when is the tension of the string at its maximum?

 

[himanshu121]

1. Tension is max at the bottom of the vertical surface and is given by
$$T_{max} = W +\frac{mv_{0}^2}{L}$$

2. N is Normal Reaction and it varies as

$$N = W\ cos\theta + \frac{mv^2}{L}$$

where \theta is the angle of astronaut with the vertical at any instant

Since its normal rxn is varying with theta , so its weight registered is also varying
so u can solve it for $$\theta =0$$ and N= W/2