Question

The total mechanical energy of the roller coaster cart below at Point A is 180,000 J. The speed of the cart at Point B is +20 m/s. Assume no energy is lost due to dissipative forces such as friction. The velocity of the roller coaster cart is +16 m/s at Point C. What is the height (in meters) of the roller coaster at Point C?

Answer 1

ME a = 180,000 J

Point B

PE = 0 (no height)

KE = 1/2 m v^2

KE b = ME b

1/2m (20)^2 = 180,000

m = 180000/ 200

m= 900 kg

Point C

vc = 16 m/s

MEc = PEc + KEc

180,000 = mgh + 1/2 m v^2

180,000 = 900 (9.8) h + 1/2 (900) 16^2

180,000 = 8820h + 115.200

180,000 - 115,200 = 8820 h

64,800 = 8820h

h= 64800/8820

h c = 7.34 m