Question

A small sphere of mass mand radius ris released from rest at A and rolls without sliding on the curved surface to point B where it leaves the surface with a horizontal velocity. Given: a = 1.9 m and b= 1.2 m. Determine the speed of the sphere as it strikes the ground at Cand the corresponding distance c [You must provide an answer before moving on to the next part.) The speed of the sphere as it strikes the ground at Cis m/s.

Answer 1

The given problem can be solved in two steps. Firstly by applying the principle of work and energy between A and B to find velocity at B and then applying equations of motion between B and C to find the velocity at C and the horizontal distance c. Please have a look into the attached images for solution in details. Thank you.

Given dada 1 loom, b= = 1.2m. mass of the ball am and radius ir Let ad a. position I al B position 2 B L 2 С b d at C so 32 ܠ k Applying ener merge - ot mg mg (bta) => position 3, Reference line the poinciples of work and bean- een position and position 2, Ty tunc Tz tuz Tat mgb ( since the bell is coeleiesed troom need, so 550) Tea mga 1 m ² + 1/ / I w² mga (since at 2, the KiE is both translational and rotational angeles vebauty ay I moment of dinertia of sphere about it's c.G (Centre of gravity) 2/3 mo? where w= angeles mass ML o f must + x max y mga } » / 20 m Vz² = nga V2 => 10 *9.81x1.99 - 5.16 m/s

Na Vyz Vaz -i Froom position. 2-3 . . The path of the bell will from poojectele motion, As Edrs s given that the ball leaves the surface with a horizontal velocity, so Yuz = 5.16 m/s and We know that throughout throughout the projectile motion, horizontal Component or relocely demoins constant. => Vaz 5.16 m/s Applying equation of motion in reotiedl direction Vyz = Vyz -gxt = o-gt=-gt (+: time taken also 2 to 3 and be Vypt +4xgx t O+ + 2x gxt² >> Z => Ł: 0.4946 sec the value or t peaking e equation 1, -gt - 9.81% 0.4946=-4.852 m/s so nel velocity at ca Svas Vaz tu => ₃ = Ve (5.16) +(-4.852 5232 => VC- 7.08 3 m/s In horizontal direction Woite, c = ln xt - 5.16 x 0:4946 3.) 12 s 2x1.2 9.81 Nys 2 13 2 Va ne con ult → С 2. 552 m