Question

When a roller coaster went upside down at the top of a loop with a radius 8.0m, a speed of 11.2m/s was required to make the coaster feel safe.

A. Assuming that air resistance and friction are negligible , what speed will the roller coaster have when it is right-side up at the bottom of the loop?

B. The roller coaster begins its trip by being pulled up the lift hill by a chain lift and dropped after it reaches the top. Determine the height of the hill required to accomplish this.

C. The lift is angled at 55⁰ with respect to the horizontal. What force does the chain lift exert in order to pull the coaster train up that hill?

I'm having trouble with this set of physics problems , any help would be appreciated. I calculated 20.95m/s for part A but unsure about part b and c

the mass of the roller coaster train is 700kg

Answer 1

The safe speed of a roller coaster train at the top most position of a loop of known radius is given. It is required to find 1) the speed of the train at the lowet position of the loop 2) height of the lift hill to which the train must be pulled up before journey and 3) force exerted by the lift chain. We use conservation of energy to solve the first two questions and resolution of forces in their component to answer the second question.

Mass mz7ool 80 m. A 0 of the roller coaster train Radius of the loop, Rz speed at the top , , , 11.2 m/s Taking of potential energy to be at the bottom of the loop, we get hey applying conservation of energy, mier toz mg. 2R :2 R + Im "? where uz is the speed at the bottom 1 2 2 2 Y " 2 14 g Rt MI g u 24 x (9.81 m/s^) (8.0m) + (11.2 m/s) (rounded to ist 2 26.9609m/s 210 m/s decimal place ) the speed at the bottom of the doop 2 210m/s (Answer) (B) Let the height of the hill be h. Then by conservation of energy, Otom mghiz (20.960 9 m/s 22.3934 m 2 x (9.81m/s2) mu to 2 h z 2 2g 224 m the required height of the hill = 22.4 m (Auswer)

F mgrino mg Let F be the force exerted. 550 the train for lifiting ing sing 2 (700 kg) (9.81 m/5²) (sin 55°) F 2 N 5625'117 N 56251 N (rounded to get decimal place) required force ? (Answer) N 5625.1