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Homework5-help

# Homework5-help - Homework 5 help 1 A bullet is shot through...

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Homework 5 help 1) A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T. The speed of bullet is 2 D V T π θ = 7.24. Model: Model the child on the merry-go-round as a particle in nonuniform circular motion. Visualize: Solve: (a) The speed of the child is v 0 = r ω = (2.5 m)(1.57 rad/s) = 3.93 m/s. (b) The merry-go-round slows from 1.57 rad/s to 0 in 20 s. Thus 2 0 10 1 1 (2.5 m)(1.57 rad/s) 0 –0.1965 m/s 20 s t t ar ta rt ωω == + ⇒ = = = During these 20 s, the wheel turns through angle 2 22 10 0 1 1 0.1965 m/s 0 (1.57 rad/s) (20 s) (20 s) 15.7 rad ( 2 . 5 m ) t a tt r θθ =+ + = In terms of revolutions, 1 = (15.7 rad)(1 rev/2 rad) = 2.50 rev. 7.47. Model: Model a passenger as a particle rotating in a vertical circle. Visualize: Solve: (a) Netwon’s second law at the top is 2 T rr mv Fnwm a r =+= = 2 T mv nm g r = ⇒+ The speed is ( ) 28 m 2 11.17 m/s 4.5 s r v T == =

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() 2 2 2 11.17 m/s 55 kg 9.8 m/s 8 m T v nm g r  ⇒= −=   = 319 N That is, the ring pushes on the passenger with a force of 319 N at the top of the ride. Newton’s second law at the bottom: 22 2 BB 2 2 11.17 m/s 55 kg 9.8 m/s 1397 N 8 m rr mv mv v
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Homework5-help - Homework 5 help 1 A bullet is shot through...

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