Question

The figure below shows a "conical pendulum", in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.050 kg, the string has length L = 0.66 m and negligible mass, and the bob follows a circular path of circumference 0.86 m.

Cord Bob (a) What is the tension in the string? (b) How much time does it take for the bob to complete one full circle?

Answer 1

Solution: Length of the string is, L-0.66m Mass of the bob is, m-0.050 kg circumference is 227 = 0.6m From the above r would be, 0.6m 2π 0.099 m a) What is the tension in the string? For finding tension the resolution would be, Tsin θ = mg → Where gis the acceleration due to gravity -9.81m/s The angle θ can be calculated as, tan 8-

0.66 0.099 - 6.90 8tan (690) -81.75 By plugging the above values in 1), Tsin(8179)=( , 0.050kg)(9.81m/s (0.050kg 9.81m/s sin (81.75°) T = 0.495 N The tension in the string is 0495

b) How much time does it take for the bob to complete one full circle? Time period is, 2xr(2) The velocity would be calculated by using, mv 0.050kg)v (0495N)cos(15.099m Solving for v, v 0.3753 m/s By plugging the above values in (2) 0.6m 0.3753 m/s -1.602s