r 240 ft 90 f Fig. P13.41 and P13.42 13.42 A section of track for a roller coast

Question

r 240 ft 90 f Fig. P13.41 and P13.42 13.42 A section of track for a roller coaster consists of two eircular ares AB and CD joined by a straight portion BC. The radius of AB is 90 ft and the radius of CD is 240 ft. The car and its occupants, of total weight 560 lb, reach point A with practically no velocity and then drop freely along the track. Determine the maximum and minimum values of the normal force exerted by the track on the car as the car travels from A to D. Ignore air resistance and rolling 0.8m resistance 0.4 m 7 13.43 A small sphere B of mass m is released from rest in the position shown and swings freely in a vertical plane, first about O arid then about the peg A after the cord comes in contact with the Determine the tension in the cord (a) just before the sphere comes in contact with the peg, (b) just after it comes in contact with the peg Fig. P13.43

Explanation / Answer

At A, normal force Na = 560 lb

At B, Nb = mgCos40- mVb^2/Rb

But 1/2*mVb^2 = mgHb

So, mVb^2 = 2mgHb where Hb = 90 - 90Cos40 = 21.056 ft

So, Nb = 560*Cos40 - 2*560*21.056/90

Nb = 166.95 lb

At C, Nc = mgCos40 = 560*Cos40 = 428.98 lb

At D, Nd = mg + mVd^2/Rd

But 1/2*mVd^2 = mgHd

So, mVd^2 = 2mgHd where Hd = 90+60 = 150 ft

So, Nd = 560 + 2*560*150/240

Nd = 1260 lb

Max. normal force is at D = 1260 lb and min. normal force is at B = 166.95 lb

Please rate my answer, good luck...

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