# Centripetal forces

**1. The problem statement, all variables and given/known data**

A 1.5 kg mass tied to the roof rotates with constant speed in a horizontal

circle. The string makes an angle of 30 deg to the vertical.

a) determine the velocity , the centripetal acceleration and the centripetal

force on the mass.

b) determine the tension in the string.

c) say the mass is given a push so that now the mass rotates with a constant

velocity of 9.4 m/s . Determine the angle the string makes with the vertical

, the centripetal force on the mass and the tension in the string.

**2. Relevant equations**

∑F_{radial} = TsinΘ = mv^{2}/R

∑F_{y} = TcosΘ – mg = 0

**3. The attempt at a solution**

To solve part a:

First I found my R by,

R = LsinΘ = 1.5sin30° = .75m

Second my T by,

T= mg/cosΘ = 1.5*9.8/cos30° = 16.97 N

Now I find my velocity by,

V= sqrt((R*T*sinΘ)/m)) = sqrt((.75*16.97*sin30°)/1.5) = 2.06 m/s

the centripetal acceleration,

v^{2}/R = a

a = TsinΘ/m = 16.97*sin30°/1.5 = 5.66 m/s^{2}

for part b I already found my tension to be 17N.

Part C is where I am having trouble, how can i find the angle Θ with the new constant velocity if im not given a radius or tension?

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