Question

1. (20 points) A pendulum consists of a small ball of mass m=2.00 kg that is suspended from a fixed point by a light string of length L=0.850 m (like the demonstration video.) The pendulum is released from rest when it is in its initial position with 0 =65.0°. Air resistance is negligible. a) Calculate the work done by gravity as the ball moves from the highest point of its semicircular path to the lowest point of its path. b) Calculate the tension in the string at the instant the pendulum moves through the lowest point of its semicircular path. L m

Answer 1

velocity at every parent m=2kg • mass L m. of ball 12=0.850m Glength of IL-28030) string 0= 65° > Initial angular position. @ Gravitational force mg will be always downward Cvertical). So, work done by gravity is equal mg x (vertical desplacement.} i Wo= max(L-LC030) L-L cose is decrease en heeght for penderlum ball. :: Wg= mgl. (1-6058)= myl. (1–cos 650) - Wy = 2x9.8x0.85* (1 - Cos 659) I uz= 9.629 D Work done by tension will zero because fengion T is perpendicular to instantaneous If relocity at lowest point is a then cs from work energy theorean,

2 L mr. > mgLCI-C0565°)= { mu? >>12 mg (1-cosas) = mu? me AT V mwa along force) "T-mg= ( centripetal T= mv 2 ting 2 &T= 2mg (1-605659) +mg »T= 3mg, 2mg cos650 [134289.8)– (2x2x9.8) Cas 650) &T= त CS sahned with CamScanner