Ip a solid sphere with a diameter of 0.19 m is released from rest; it then rolls without slipping down a ramp, dropping through a vertical height of 0.61 m. the ball leaves the bottom of the ramp, which is 1.22 m above the floor, moving horizontally.

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Mathematics

Kaydence Valentine

2 April, 23:06

Ip a solid sphere with a diameter of 0.19 m is released from rest; it then rolls without slipping down a ramp, dropping through a vertical height of 0.61 m. the ball leaves the bottom of the ramp, which is 1.22 m above the floor, moving horizontally.

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Gilmore · Answer 1

Answer: K = (1/2) mvÂ˛ + (1/2) IĎ‰Â˛, where m is the ball mass, I is the ball's moment of inertia (2/5) mrÂ˛, and Ď‰ is the angular velocity of the ball. Because the ball rolls without slipping, it is easy to see that v=Ď‰r, or r=v/Ď‰. Then, K = (1/2) mvÂ˛ + (1/2) (2/5) mrÂ˛Ď‰Â˛ = (1/2) mvÂ˛ + (1/5) mvÂ˛ = (7/10) mvÂ˛ Setting potential at the top equal to kinetic at the bottom, mgh = (7/10) mvÂ˛ v=âš{ (10/7) (gh) } = [ (10/7) (9.8) (0.51) ]^ (1/2) = 2.672m/s