Question

If a rollercoaster with a weight of 9,000 pounds is at a hight of 100ft. What is its velocity at a point 26 feet above the bottom of the track if it has lost 3,000 ftlbs of energy?

Answer 1

Given Il a rollercoaster with a weight is 10 w = 9000 lbs = 14.086 kq (1 lbs= 0.4546 hap his goofton velocity at point 26 it above the bottom of the track ie. 126ft = uz? I roller coaster lost 3000 ft lbs energy The rollercoaster at initally rest at point A ( Suppose) pag using the concept q law Of cons. ervation f energy - e. A omfs. (Above eft + 26ft looft C Conseguation 9 energy EEA = ER I PEA+KEA = PEB + KEB mg hat 1 m (UA) = mg HB t / m (wp² ub= Juate gaa 12gHA VA - O mis Since ccleration due gravity = 32.2 Ft/ see = |2x32.2 x Too I = 6440 UB = 80.24 Ft/sec

Since at pt point B P E. is transfer to KIE. {EB = { Efinal KEB = P. E final I made my 4finat Hain (08)? 4 I Final = 0.5x ( 80.24)2 32.2 Hfinal = 99.9760 Ft The coaster does not going out enough At what velocity need to reach at point eie above 26 ft from bottom 9 track Dall energy at point A is transfered. to p.E at a EA - SE - PEATKEA = PEC but PFA is given ie 3000 ft lbs mq 4 t I mu 2 = mghe 2 ses YA = 126 x 32.2 - 3000 - 4057,2-3000 A2 = 1057.2 UA = 32.5147 Ft / sec. Since at 32.5147 Ft/sec velocity need at 26 ft above the bottom a track.