Circular motion, help pleaze :(?

Question

a child is swinging on a maypole in a playground. when the child, mass of 40 kg, is moving at a constant speed of 5.o m/s the rope makes an angle of 30 degrees to the central pole. the center of the mass of the child moves in a horizontal circle of radius 4.3 meters

what is the magnitude of the net force acting on the child? (answer is 233N)

what is the tension in the rope (assumin mass of rope is negligible) (answer is462N)

i dont know how to work it out any help would be greatly appreciated. thankx

oxo

Answer 1

use the equation:

force pulling the child towards the centre of the circle and keeping him in orbit is called the centripetal force;

centripetal force = m*(v^2)/R

                      m= mass

                      v= velocity

                      R= radius

             ***** F= 40*(5^2)/4.3 = 233 N

the above fromula will solve the first part ...just substitiute the variables,.....

Then:

  if you make a simple diagram showing the 30 degrees that the rope makes with the pole, and since the child is in vertical equilibrium( does not move up or down) ... then ,,

       ***** upward forces = downward forces

              

(    it will be like this )

                  40 * g = T * sin 60

(g = 10 ) acceleration due to gravity;;

                 40 * 10 = T* sin 60

                  T= (40*10)/sin 60 = 462 N

HOPE THAT HELPED :))