Question

Problem 4: Given the following, three of four shapes (1) hoop (ii) cylinder (ii) sphere and noting that they all have the same radius, mass and are released from an incline; solve for the velocity at the finsih line if the height/elevation is 1.0 m. С Figure 1. (Left) Analyze only hoop, cylinder and sphere (right) detailed view

Answer 1

mass m radimir H 0 © Let on an consider a general body of any shape which rolles down inclined plane from rest at position og let V at bottom . be the relocity By law of total energy conservation of energy, 사 position o total energy of body at position o I mv²t II w? without slipping. mgh 2 2 Assume > that body rolles down Vera r I mk² Also, about quis where, ks Radius of gyration rotation. I (mk?) ( Įmv? + mgh 2 gH -v? [1+ 2

2 2 g H . [ + ķ] V = 2gH (+ ķ at bottom point or finish line .. velocity V= 2gH (it K² ) 0 Hoop for hoop, k = R =r va 2gH ан ?? (1+ H=1m put g = 9.81 m 52 i', 9.8X1 V = : 3.132 m V

© Cylinder ㅗ 2 for cylinder, k= r therefore 14 = 2g H 2gH 1. V = = H+ - Z It k² 82 . i. Va --X 9.81X1 1 / gh m v = 3: 617 S (3) sphere T 11 r for sphere, G/N k? = Ult 2 V = 2gh 1+k² 2gH 1+ lo JH 7 Lex 9.81X1 V =3.744 m 5