After you pick up a spare, your bowling ball rolls without slipping back toward

Question

After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of 3.05 m/s, as shown in the figure below. To reach the rack, the ball rolls up a ramp that rises through a vertical distance of h - 0.509 m. What is the linear speed of the ball when it reaches the top of the ramp? (in m/s) A: 7.99x101B: 9.03x1011.02D: 1.15E1.30:1.47 G: 1.66H: 1.88 Submit Answer Tries 0/3 If the radius of the ball were increased, would the speed found in part (a) above increase, decrease, or stay the same? If the radius of the ball were increased, the speed would decrease. If the radius of the ball were increased, the speed would stay the same. If the radius of the ball were increased, the speed would increase. Submit Answer Tries 0/3

Explanation / Answer

a) Krot = 1/2 I w2

Krot = 1/2 (2 / 5 M R2) (v/R)2

Krot = 1/5 M v2

kinetic energy Ki = 1/5 M v2

rotational kinetic energy Krot,i = 1/5 M v2

potential energy Uf = M g h

kinetic energy Kf = 0.5 M v'2

Krot,f = 1/5 M v'2

From conservation of energy

1/2 M v2 + 1/5 M v2 = M g h + 1/2 M v'2 + 1/5 M v'2

7/10 v2 = g h+ 7/10 v'2

7/10 * 3.052 = 9.8 * 0.509+ 7/10 v'2

v' = 1.47 m/s [option F]

b) if radius of ball were increased, speed would stay same

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