A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?
Mass of the stone, m=0.25 kg Radius of the circle, r=1.5 m Number of revolution per second, n=40/60=2/3rps Angular velocity, ω=2πn The centripetal force for the stone is provided by the tension T, in the string, i.e., T=mω2r =0.25×1.5×(2×3.14×(2/3))2 =6.57 N Maximum tension in the string, Tmax=200 N Tmax=rmvmax2 vmax=(mTmaxr)1/2 =(200× 1.5/0.25)1/2 =(1200)1/2 = 34.64 m/s Therefore, the maximum speed of the stone is 34.64 m/s.
