Question

Two boxes are connected to a rope, and the rope is hung over a pulley connected to the ceiling, as shown in the figure below.

The masses of the boxes are m1=18.0 kg and m2=12.0 kg, the mass of the pulley is M=5.00 kg, and the radius of the pulley is R=0.300 m. Box m2 is initially on the floor, and box m1 is initially 4.70 m above the floor when it is released from rest. The pulley's axis has negligible friction. The mass of the rope is small enough to be ignored, and the rope does not slip on the pulley, nor does it stretch.

(a) How much time (in s) does it take box m1 to hit the floor after being released?

(b) How would your answer to part (a) change if the mass of the pulley were neglected? (Enter the time, in seconds, it takes box m1 to hit the floor if the mass of the pulley were neglected.)

Answer 1

Answer: givendata m=18kg , m = 12 kg, M=5kg, R=0. 3m, h=4.7m (a) from Newton's second law migatia maa Tz - Meg = M₂ a YT-VT2 = t - ura x = 9 T-T2 = ; на How soling the system of three equation for a we get- a=g(mi-ma) (mith,+12M) = 9.81(18-12) (18+12 + 2 / 2 ) a=1.81m18 Aterler = 1/2x467) VO 1:81/ ::.45,=2.285 (6) when mass of Pulley ignored a=9(mi-ma) - a mitme) 9.81(18-12) (18+) a = 1.96 m/s rate 2019 s