A horizontal 810-N merry-go-round of radius 1.60 m is started from rest by a con

Question

A horizontal 810-N merry-go-round of radius 1.60 m is started from rest by a constant horizontal force of 50 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry- go-round after 3.0 s. (Assume it is a solid cylinder.) Your response differs from the correct answer by more than 10%. Double check your calculations. Need Help? A constant torque of 28.0 N. m is applied to a grindstone whose moment of inertia is 0.130 kg. m2. Using energy principles, and neglecting friction, find the angular speed after the grindstone has made 18.0 revolutions. Hint: the angular equivalent of Wnet = F Delta x = 1/2mvt2 - 1/2mvi2 is Wnet = tau Delta theta = 1/2I omega t2 - 1/2I omega i2. You should convince yourself that this relationship is correct. (Assume the grindstone starts from rest.) rev/s Need Help? Four objects-a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell-each has a mass of 5.13 kg and a radius of 0.239 m. Moments of Inertia for Various Rigid Objects of Uniform Composition

Explanation / Answer

10)T = Fxr

T = 50x1.6 = 80Nm

= T/I

= t = 3 = 3T/I

K.E = 0.5 I 2 = 0.5 x 9T2/I

I = 810/9.8 x 2.56 = 211.6

K.E = 3200 x 9/211.6 = 136.106 J

11) T = 28

I = 0.13

= 28/0.13 = 215.446

= t = 215.446t

d/dt = 215.446t

= 107.7t2

36 = 107.7t2

t = 1.05sec

= 226.243 rad/s = 36 rev/s

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