Question

1. A roller coaster has a 300 kg car. Assume the track is frictionless. a) The car starts at a speed 20 m/s on a horizontal track. It then goes through a circular loop. What is the speed of the car when it is at the top of the loop, h = 10 m above the horizontal track? b) What is the normal force applied from the track at the point? Does this force point upward or downward? Assume the track is perfectly circular, with a radius R = 5 m. 2. A box of mass 5 kg sits at the bottom of a ramp at incline of 15°. The box's coefficient of kinetic friction with the ramp is 0.1. It's attached to a rope which is held over the side of the ramp by a frictionless pulley. A Force of 70 N is pulled down on the rope. a) The box on the ramp begins to slide up the ramp. Find the work done by gravity by the time it reaches the top, which is L = 5 meters along the ramp from the bottom. Do this 2 ways, once using W, = Fgscos(o) and another use W, = -AU. b) Use Work-Energy theorem to find the speed of the block when it reaches the top of the ramp.

Answer 1

feel free to drop comment if you have any doubt.

(a) CO) by energy conservation 2 por ? = wig (22) + 1 Jn ve ² V2² - v,2 29 (2R) (2R=h= lo mi Vz? = (2012, 2x9.8 xl 10)

V₂ = 14.28 mn S cb) F.B.D. Force Balance N mg NT mg = 9 = my? N t 300 x 9.8 = 300 X (14.28)² IN = 9300 downward