Question

A me=30-kg reel is mounted on top of a cart using a frictionless bearing at its shaft 0. The shaft is centered on the cart wheel base: H=400 mm, W=500 mm. The reel radius of gyration about the shaft through its mass center O is ko=250 mm. The cart's mass is me=40-kg with a center of gravity 80 mm above the base platform underneath 0. The cart rolls on idealized wheels whose dimensions are negligible. Starting from rest, the cable wrapped around the inner hub of the reel (o=150 mm) is subjected to a constant force P=50 N. FIND: (A) Draw appropriate Free Body Diagram(s) for the reel and cart; (B) The VELOCITY Lo(t) of the cart as a general function of time and specifically at t = 4 seconds; (C) The ANGULAR VELOCITY 08(t) of the reel as a function of time and specifically at 1 = 4 seconds; (D) The complete REACTION (R.) at the bearing O. m mc

Answer 1

Solution → 30 kg MR= H = 400 mm 500 mm Ginen 250 mm Ko Mc = 40 kg To 150 mm pa SON (A) FBD Free body diagram Ry Rr RA p=50N RH meg 1 R meg Reel Cart

from FBD of reel RH 50N mag 30x9.81 Ev = 294.3 N Torque Paro T sox 150 7.5 Nm 103 IT = 7.5 N-m From FBD of Curt 2R mcg + Rv AR 40x9,81 + 294.3 343.35 N (B) Net force ( Horizon tel ) = (M) system * acceleration RA (40+30 ) X 50 70 a a = Now applying 5/4 m/s² laws of motion equation ut at { was system at rest initially 0 + Sot Sxt U=0 5 t at t = 4 sec 4 20 -) Vo = 2.857 m/s

(C ) Applying Torque 2 7.5 Ia Mai (ko) x x 30 (0.25) 2 7.5 2 = 4 rad/s2 Now, ملی - Wi tait (w==0) Wf = 4 t W(+) 4 t at t= į see 4x4 = +6 rad, Angular velocity 26 rad/s (D) Complete reaction at bearing Ro ✓ Ry² + R² Ro 2 (294.3 )? +(50) Ro 298.52 N # so Complete recetion (Ro) at the beasing is given by 0 298.52 N.