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
∑Fradial = TsinΘ = mv2/R
∑Fy = 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,
v2/R = a
a = TsinΘ/m = 16.97*sin30°/1.5 = 5.66 m/s2
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?