Hibbeler chapter 19, impulse and momentum of a rigid body. Please be neat so I c

Question

Hibbeler chapter 19, impulse and momentum of a rigid body. Please be neat so I can follow!

The 25-kg reel is mounted on the 18-kg cart If the cable wrapped around the inner hub of the reel is subjected to a force of P = 50 N determine the velocity of the cart when t = 3.9s . The radius of gyration of the reel about its center of mass O is ko = 250 mm. Neglect the size of the small wheels. Express your answer to three significant figures and include the appropriate units. Determine the angular velocity of the reel when t = 3.9s Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

equating forces :

F=(M+m)a

50=(25+18)a

a=1.1627m/s2

initial velocity u=0m/s

velocity at t=3.9s is v

v=u+at

v=1.1627x3.9=4.5348m/s

torque acting on wheel = Fxr = I(aplha) = 50x0.15

25x(0.25)^2 (alpha)= 50x0.15

angular accelaration = alpha = 4.8 rad/s2

w' = w + alpha x t = 4.8x3.9= 18.72rad/s

velocity of rope = v+rw = 4.5348+0.15x18.72= 7.3428m/s

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