A mass M = 4 kg attached to a string of length L = 2.0 m swings in a horizontal circle with a speed V. The string maintains a constant angle \theta\:=\:θ = 26.2 degrees with the vertical line through the pivot point as it swings. What is the speed V required to make this motion possible?
here,
mass , m = 4 kg
length of string , L = 2 m
theta = 26.2 degree
the radius of circle , r = L * sin(theta)
r = 2 * sin(26.2) m = 0.883 m
let the tension in the string be T and speed of mass be v
equating the forces vertically
T * cos(theta) = m * g
T * cos(26.2) = 4 * 9.81
T = 43.7 N
equating the forces horizontally
T * sin(theta) = m * v^2 /r
43.7 * sin(26.2) = 4 * v^2 /0.883
solving for v
v = 2.06 m/s
the speed required to make this motion is 2.06 m/s