(b) (d) (a) Height of the firnt hill- Shape of the firnt hill The axit path The loop Figure Q2(a) Profile of roller coaster: (a) The height of first hill height 20m, (b) Shape of the first hill and radius at the bottom p = 60 m, (c) The exit path height 5m, and (d) The loop to end the ride is a level ground, ignore the small height.
(a). You are required to design a roller coaster with the profile shown in Figure Q2(a).
An electric motor will pull the coaster to the top of the first hill. After the coaster has been pulled to the top, no more external work will be added to it. Hint: the amount of energy the coaster has to complete its journey on the track depends on the potential energy on the first hill. This will give you the relationship between the height of this hill and the speed of the coaster.
The shape of the first hill will determine if the coaster will safely travel on the track and speed of the coaster. Hint: you can imagine the coaster as a particle that moves in space along the track in a projectile motion.
The coaster exit through a second hill to maintain feeling of speed and thrill in the ride. The second hill is also to maintain the speed to the next stage of the ride. Hint: the safety of travel on the track depends on the speed you are travelling and is related to the hill you are coming from.
Instead of adding a loop to your coaster, the coaster is allowed to gradually cruise to a stop. Assume is a flat path.
Assuming a total mass of 1000kg, explain with calculations how would you design the roller coaster from start till the end of coaster ride:
(iii) the radius of the exit hill and stopping distance of the coaster at the end of the flat path, assuming a braking force 1500N is applied.
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