1. (a) A uniform cylindrical bar of mass 400 kg and radius 0.16 m is rolling wit

Question

1. (a) A uniform cylindrical bar of mass 400 kg and radius 0.16 m is rolling without slipping at 6 m/s. Find (0 the translational KE, (t) rotational KE, (rr'D total KE [10.8 kJ]. (b) The bar rolls up an incline: (r) What is the maximum height? (tt) ls the force of (static) friction directed upor downlhe incline? ls the friclional torque in the salre or the oppositesense to the angular motion? (Static friction does no net workhereit effectivefy transfers energy from rotation to translation.) (c) The experiment is repeated on a frictionless incline. Now the spinning cylinder sriy'es up-the angular velocity remains constant, with rotation decoupled from translation. What is the maximum height? (As the cylinder slides back down the incline, how would it be evident to an observer that it wasn't rollinq?)

Explanation / Answer

given

mass m = 400 kg

radius r = 0.16 m

the speed v = 6 m/sec

the moment of inertia is I = 0.5 m r2

= 0.5 X 400 X 0.162

= 5.12 kg m2

the KEtranslational = 1/2 m v2

= 0.5 X 400 X 62

KEtranslational = 7200 J

KErotational = 0.5 m v2 X ( k/r )2

( k/r )2 = 1/2 for the cylinder

so KErotational = 0.5 m v2 X 0.5

= 0.52 X 400 X 36

KErotational = 3600 J

KEtotal = KEtranslational + KErotational

KEtotal = 7200 + 3600

KEtotal = 10800 J

so KEtotal = 10800 = m g h

10800 = 400 X 9.8 X h

h = 10800 / 400 X 9.8

h = 2.755 m

and

KEtranslational = 7200 J = m g H

H = 7200 / m g

H = 7200 / 400 X 9.8

H = 1.83673 m

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