Use Impulse momentum method to Calculate new values Ra and Rb exerted by the fra

Question

Use Impulse momentum method to Calculate new values Ra and Rb exerted by the frame on the shafts.

With the gears initially at rest and the couple M equal to zero, the forces exerted by the frame on the shafts of the gears at A and B are 30 and 16 lbs, respectively, both up ward to support the weights of the two gears. A couple M = 60 lb-in. is now applied to the larger gear through its shaft at A. After 4 seconds the larger gear has a clockwise angular momentum of 12 ft-lb-sec, and the smaller gear has a counterclockwise angular momentum of 4 ft-lb-sec. Calculate the new values of -the forces Ra and Rb exerted by the frame on the shafts during the 4-second interval. Use the impulse-momentum method.

Explanation / Answer

L =r x p

whee x is the vectorial product.

For the big wheel

delta(L1) =R1*delta(p1)

delta(p1) = Delta(L1)/R1 =12/8 = 1.5 lb*s

for the smaller wheel

delta(p2) =Delta(L2)/R2 =4/5 =0.8 lb*s

Variation of force on shaft A acts to accelerate the small wheel.

F(A) =F1(0)+ Delta(P2)/Delta(t) =30+ 0.8/4 =30.2 lb

F(B) =F2(0)+(Delta(P1)/Delta(t) =16+1.5/4 =16.375 lb

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