here,
mass , m = 8.1 kg
length , l = 1.15 m
radius of the circle , r = l * sin(theta)
r = 1.15 * sin(theta)
tangential speed , v = 2.403 m/s
let the tension in the string be T and angle be theta
equating the forces vertically
T * cos(theta) = m * g .....(1)
and
equating the forces horizontally
T * sin(theta) = m * v^2 /r ....(2)
from (1) and (2)
tan(theta) = v^2 /rg
tan(theta) = 2.403^2 /(1.15 * sin(theta) * 9.81)
solving for theta
theta = 38.9 degree
the angle with vertical is 38.9 degree
3)
radius , r = 6370 km = 6.37 * 10^6 m
mass of Earth , m1 = 5.98 * 10^24 kg
m2 = 33000 kg
the magnitude of force , F = G * m1 * m2 /r^2
F = 6.67 * 10^-11 * 33000 * 6.37 * 10^6 /(6.37 * 10^6)^2 N
F = 0.35 N
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