angle of rope from vertical = A
R = 7
T cos A = m g
T sin A = m v^2/R
so
tan A = v^2/(g R) = v^2/(9.81*7)
but we are given that sin A = 7/13 so A = sin^-1 (.538) = 32.6 deg
so
tan A = .639
so
.639 = v^2/(9.81*7)
A child finds a rope hanging vertically from the ceiling of a large storage hangar. The child grabs the rope and starts running in a circle. The length of the rope is 13.0m. When the child runs in a circle of radius 7.0m, the child is about to lose contact with the floor. How fast is the child running at that time?
1 answer
3 answers