Question

8. A solid wooden door, 90 cm wide by 2.0 m tall, has a mass of 35 kg. It is open and at rest. A small 500-g ball is thrown perpendicular to the door with a speed of 20 m/s and hits the door 60 cm from the hinged side, causing it to begin turning. The ball rebounds along the same line with a speed of 16.0 m/s relative to the ground If the momentum of inertia of the door around the hinge is I=1/3 Ma’, where a is the width of the door, how much energy was lost during this collision? A) 30 J B) 16 J C) 15 J D) 13 J E) 4.8)
ANSWER: A

please show work thoroughly by writing it out!!

Answer 1

initial ongaiqr omentun Ldoor L bal1 LI O mV r o +o-5x20 x0-6) 6Kgm2/s Final aungular momen tum LF Ldoor tL ba I tm V2 Y 6.SX 16X 0.6 x0-go x 2 t 0 54 4 8 by momentum Li= con gervation LA 6 O.Sy W4 8 2.2 ad /se c mv m r us) 0.9 x 20-0.9 x 162-0.54x (2.2)2 Erost 2 E tost E10St 30 J 2.2