Question

Kim whirls a 10 kg bag, which is connected to a string in a horizontal circle above her head at some unknown constant speed v. Suddenly, the string breaks and the bag flies off and lands 10 m away with a time of flight of 0.5 s. If the string was 1.5 m long,

a) What was the speed of the rock before the string snapped? (vertical motion irrelevant)

b) Find the tension in the string before it snaps.

Answer 1

When the string breaks, let us assume the speed =v

since the range of flight is 10m with time of flight =0.5s

speed of the bag = distance/time = 10/0.5 =20m/s (because there is no acceleration in the horizontal direction after the string breaks)

When the bag is rotated,

Forces acting on the bag are tension=T due to string and centrifugal force acting on the bag in outward radial direction.

Centrifugal force = mv^2/r where r is length of the string

so, T=mv^2/r = 10*20*20/1.5 =2666.67N=2.67kN