Question

Part A A size-soccer ball of diameter 226 cm and mass 426 grols up a hill without slipping, reaching a maximum height of 6.50 m above the base of the ML We can modelis ball as a thin walled hollow sphere. You may want to review (Pages 309-315) For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Acceleration of a rolling sphere At what rate was rotating at the base of the har? ΠΙΑΣ rad/ Sub Press the X Incorrect; Try Again; 4 attempts remaining - Part 3 How much rotational kinetic energy did then have? AE ? J Kro- Submit Previous A Beast X Incorrect; Try Again; 3 attempts remaining

Answer 1

old so 0.426 kg Q. Given Ball (Hollow sphere) has Rodius The Diameter Ps D= 22.6cm R = 22.6 11.3cm 2 R = 0.113m The mass of Ball initially =w (let sey The Ball is Pottating with the angular velocity The Ball has toorslational motion so The Kinetic energy of Ball only due to Rotational motion so initial Kinetic is Where Iw" energy moment of inertia about exis. (center of nass) initally Ball at Base is he I 2/ m R² finally Ball at top of hill final height hoh h=6.5om and ball reaches at moximum height ho so it does not have any Rotational Kinetic energy finally finally so final Kinetic energy zero il ke ure (TE) Conservation (No Rotation at Krok So height with Total energy meximum height hf=h Ball stops) Rotating hp=0 Base Pritiall (TE I final PE final (TElimit KEP t PE, = KES KEJ + PEF Iw" + nghi o tinghe Potential of Boll energy

' The SO The final Kinetic intial kinetic (Rotational) energy of Bait I I Wp? might (0.426 ) (9. 81)(650) (Kotha = 27.16 Joule (k Hotlie 2 Kinetic energy The initial Rotational of Ball is 27.16 Joule

(A) As Kotle P I = 2/3 MR? Ź Iw .) MR² w² 14 ( 22 ) ImR?W? = 27.16 S2 W² 27.16X3 27. 1683 MR? w 2 27.86 83 m R2 = 122.39 rad W 0.426 (0.113) The initial argul at speed of Ball ps Wp = 122.39 rad, radlec