Backwards Design for Roller Coaster: Projectile Motion

AI Thread Summary
To successfully design a roller coaster that projects a 5-gram marble to land 0.5 meters away, it's crucial to determine the optimal height and angle of the ramp. Utilizing conservation of energy principles will help calculate the marble's velocity at the ramp's end, which is essential for achieving the desired projectile motion. The discussion emphasizes the need to consider both linear and angular momentum, especially if the track design involves rails that affect the marble's motion. Understanding the relationship between energy, velocity, and the ramp's specifications will guide the design process. Proper calculations will ensure the marble reaches the target distance effectively.
RockThis52
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For my grade 12 physics class, we need to build a roller coaster. We are given a marble weighing 5 grams and it must be projected at the end of the track. It needs to land 0.5 m at a target when it is projected. Since the coaster is made entirely by myself the ramp in which it will be projected off must be angled and at the exact height in order for the marble to land 0.5 m away. My question is how would I find out the angle and the height of the ramp to project it given only the weight of the marble and the displacement in the x direction. Would it be wiser to figure out the velocity the marble will achieve at that point in the coaster and then adjusting the ramp to land that far away? I have no idea where to start, thanks for any help in advance.
 
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Think about conservation of energy.
Think about projectile equations.
 
Well I know conservation of energy, should I use that before I get to projectile motion? In other words, should I find out the energy and velocity and what not before the projectile than get to the projectile?
 
Complicating matters is that the marble will also accumulate angular energy as it rolls, and if the "track" is a pair of rails, the spacing between the rails will effect the ratio of angular to linear velocity.
 
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